How does Dmitri change Anna and how does Anna change Dmitri?
One way in which Anna has been changed by her affair with Dimitri is that she has come to a point where she understands the pain in consciousness. Prior to her affair, she had been living a conventional life with her "flunkey" husband. Yet, her affair with Dimitri ignited the spark of life, what it means "to live". In learning that what she wanted in life was "to live," Anna recognizes that there is pain intrinsic to such a condition. Anna is immersed in complete pain because of her love for Dimitri, but it is a pain that indicates the essence of life and what it means "to live." As a result of Dimitri's love for her she now sees herself and he as "a pair of birds of passage, caught and forced to live in different cages." There is a sweet pain to this condition of being, one that Anna now knows. While the ending is one in which we are left with more beginnings, Anna has found the essence of being in the world and the pain that goe along with that is now a pat of her condition in the world. This only happens as a result of her relationship with Dimitri.
For his part, Dimitri has been changed by Anna in how he sees himself and his place in the world. He no longer is the "casual lover" and he no longer sees women in an "inferior light." He has become changed though Anna's way of seeing him. In Anna seeing him as "kind, exceptional, lofty," he now recognizes that he must act in accordance to how she sees him. He is changed because he can no longer accept a condition of the world where there is inauthenticity evident:
...everything that was of interest and importance to him, everything that was essential to him, everything about which he felt sincerely and did not deceive himself ... was going on concealed from others; while all that was false... went on in the open.
Anna inspires in Dimitri a desire for something more than what is, an aspirational desire to transform his being in the world. It is one in which there is more pain evident, but in this new beginnings and a commencement of a new journey is also a part of this change.