the circus tent was struck by lightning. Falling, Anna grabbed a guy wire, which was superheated by lightning.  She was confined to a hospital for a month and a half, and her daughter was stillborn.  Throughout her lifetime, the narrator considered this daughter, her half-sister, as a part of her own existence, "a less-finished version of herself".

While she was in the hospital, Anna met her second husband, a doctor, who was the narrator's father.  The doctor taught Anna to read while she was hospitalized, and they fell in love.  The narrator refers to the fact that her mother gave birth to her as the second reason she owes her for her existence, this time in a literal sense.

The narrator owes her existence to her mother a third time because of an incident that occurred when she was seven years old.  The narrator was home with a babysitter when their farmhouse caught fire.  By the time her parents returned home, the house was engulfed in flames, and there seemed to be little hope that firemen would reach the narrator in her room because their extension ladder was broken.  Undaunted, Anna used the broken ladder to climb an elm tree near the house that had a branch that brushed the roof.  She crawled along a bough above the branch and leapt towards the roof, landing on it and, using her acrobatic skills, hanging from the rain gutter over her daughter's window.  Anna entered the narrator's room, and, clutching their daughter, jumped from the window into a safety net below, saving her life.

In Louise Erdrich's short story "The Leap," the unnamed narrator says of her mother, "I owe her my existence three times. The first was when she saved herself." The narrator's mother, Anna, and Anna's first husband, Harry, once formed a trapeze act called the Flying Avalons. One day, lightning struck the circus tent where the Flying Avalons were performing, and the seven months pregnant Anna had to choose between falling with her husband to their deaths and saving herself and their unborn child, the narrator's half-sister. Though Harry was killed, Anna was injured, and their child eventually stillborn, the narrator sees her mother's decision to save herself as the first time she owes her mother her life, as she wouldn't have otherwise been born.

While recovering in the hospital, Anna met her second husband and the narrator's father. He was the doctor who looked at Anna's broken arm, and he taught her to read and write in exchange for her stories of traveling the world with the circus, a life she gave up when they married. The narrator says of her parents,

I owe my existence, the second time then, to the two of them and the hospital that brought them together. That is the debt we take for granted since none of us asks for life. It is only once we have it that we hang on so dearly.

The third time the narrator owes her mother her life forms the climax of the story. The narrator recalls how, when she was seven years old, her family's house caught fire when her parents were out, leaving her trapped in her upstairs bedroom by the time her parents and a group of volunteer firefighters arrived. For just this one night, Anna tapped into her old trapeze skills to execute a flying leap from a tree branch to the gutter above her daughter's window, echoing the way she had grabbed onto a guy wire and used it to lower herself to the floor of the circus tent the night of the long-ago lightning strike. This time, Anna lowered herself into her daughter's room, scooped her up, and then leapt out the window with her in her arms, landing them both safely in the firefighters' net.

The narrator means that her mother saved her own life or her daughter’s life three times.

The story describes a trapeze artist’s daughter. She explains the impact her mother had on her life, specifically by saving her life. The narrator feels that her mother is a very unique and interesting person, and she wishes she knew her better.

The first time her mother saved her life, she actually saved herself. In saving herself, she saved her unborn daughter.  Her mother saved her life by avoiding an accident during a big windstorm.

The first time was when she saved herself. In the town square a replica tent pole, cracked and splintered, now stands cast in concrete. It commemorates the disaster that put our town smack on the front page of the Boston and New York tabloids.

Her mother was in a trapeze accident when lightning struck while she was performing. The narrator considers this the second time her life was saved, because it was in the hospital after the accident that her mother met her father.

I owe my existence, the second time then, to the two of them and the hospital that brought them together. That is the debt we take for granted since none of us asks for life. It is only once we have it that we hang on so dearly.

If her mother had died, or had not been in the accident at all, her mother and father would not have met and the narrator would not exist. So again, while saving her own life her mother saved hers, by creating the possibility of her being born.

The third time her mother saved her life was the most spectacular. There was a fire, and the narrator was trapped inside. She was only seven years old, but there was no chance of rescue. Since the firefighters could do nothing, her mother took a literal leap of faith to save her.

I didn't see her leap through air, only heard the sudden thump and looked out my window. She was hanging by the backs of her heels from the new gutter we had put in that year, and she was smiling. I was not surprised to see her, she was so matter-of-fact.

The narrator’s mother is clearly an amazing woman. Telling this story is her way of attempting to get closer to her. Her mother faces many close calls. The narrator recounts the impact that her mother had on her life through the most spectacular events in her mother’s life.

In the exposition of "The Leap," the narrator declares that she owes her mother her life: the first time is the day that her mother saved her own life; the second, that her mother married again and was in the hospital that brought her and her husband together; the third, that her mother saved her life by rescuing her from the burning house.

Certainly,the third time is the most active, powerful act of saving that the mother commits, for she directly puts herself in danger when she is none herself. In the other two instances, the saving of her daughter is secondary rather than primary: In the first instance with the lightning hitting the pole, the mother chooses to save herself, thus, saving her her unborn baby--

As he [her husband] swept past her on the wrong side, she could have grasped his ankle,...and gone down clutching him. Instead, she changed direction--

in the second instance at the hospital, the depressed mother is renewed by her love for her new husband who also rehabilitates her arm, thus allowing the mother to be a better parent to the narrator.

But, in the third instance the mother actively and purposefully places herself in immediate danger in order to save her daughter with no concern about her own safety. 

In "The Leap," the narrator owes her life to her mother, Anna, in the following three ways:

• In the first "leap," the mother saves her own life, thereby ensuring the birth of the narrator later on. In this instance, the narrator's mother was performing as part of a blindfold trapeze act called the Flying Avalons when a storm hit the circus tent. Instead of meeting mid-air, as expected, a bolt of lightning hit the main pole, causing the "edifice" to topple forward and thrust Anna's partner, Harry, to the ground. Harry lost his life, but Anna was able to climb to safety, though she burned her hands and later suffered a stillbirth. 
• In the second "leap," the narrator's parents meet and fell in love, thereby making it so the narrator could be born later. The narrator's father is a doctor who treats Anna in hospital after her first leap.
• In the final "leap," Anna literally saves her daughter's life by rescuing her from her bedroom during a house fire.

The narrator, of Louise Erdrich's "The Leap," states that she owes her mother her life for three different reasons. According to the narrator, "the first is when she saved her life." During a trapeze act with her husband, the narrator's mother "managed to hang on to the braided metal" even after it was struck by lightening. Unbeknownst to her, she was pregnant. Her ability to twist, turn, and grab the pole insured the life of the mother (the unborn child did not survive). 

The second instance where the narrator states she owes her life to her mother is when her father "found" her mother in the hospital. Her father taught her mother to read when tending to her as her doctor. It is the love which kindled between the doctor and the patient which brought about the birth of the narrator. 

The third and final time the narrator owes her life to her mother is when she saved her from a fire. When the narrator was seven, their family home caught on fire. With the fire burning out of control, the narrator's mother saves her. She leaps into the air to grab onto the roof and save her daughter. 

This is a great question. The narrator clearly tells us that she owes her "existence" to her mother three times, yet in the story she only explictly refers to the first and second way in which her mother saved her, telling us of how Anna saved herself from a tragic circus accident that resulted in the death of her then-husband, and then secondly refering to the fire that threatened to burn the narrator when she was a girl. The narrator at no stage in her narrative explicitly tells us what the third time was, however, if we look at the story and the narrator's present state and why she has come back to live with her mother, perhaps we can infer that this third time is the way in which her mother's solitude has given the narrator the excuse that she needs to flee her life and return home:

Since my father's recent death, there is no one to read to her, which is why I returned in fact, from my failed life where the land is flat.

We are given no more details about the narrator's "failed life," but given the way in which the narrator is similarly unforthcoming about the third way in which her mother saved her life, perhaps we can connect the two. The death of the narrator's father and her mother's need for somebody to read to her could have enabled the narrator to escape from what appears to be a very difficult and painful situation.