These terms are all taken from Aristotle's Poetics.
Each of these themes occur in all three plays of the trilogy. In some ways, though, the inevitable cycle of revenge which only ends with transformation of the Erinyes into the Eumenides at the end of the trilogy.begins before the action of the play with the curse of the house of Atreus which began when Tantalus cooked his own son Pelops served the flesh to the gods. Later Tantalus' grandson Atreus, the father of Agamemnon, killed the sons of Thyestes and fed them to their father. The curse gets handed down from generation to generation, until it ended at the final trial in the Eumenides.
From Clytemnestra's point of view, Agamemnon has exhibited hubris (which in Greek actually means something closer to "aggravated assault" than the popular misusage, "arrogance") in (1) his sacrifice of Iphigenia, (2) his abandonment of his responsibilities at home and (3) his returning with Cassandra. These acts, especially the sacrifice of Iphigenia, are a type a hamartia (a "spear thrown") which cannot be recalled which start an inexorable series of events. The anagnorisis, or moment of discovery, is when Agamemnon discovers that Clytemnestra intends to kill him, and the peripetia, or reversal occurs when Agamemnon, who enters the play in triumph, is killed ignominiously. Catharsis is not an act within the play, but rather the "katharsis ton pathematon" or "purification of the emotions" of the spectators to the play.
Of course, by killing Agamemnon, Clytemnestra does not ends the curse, but herself commits hubris, and begins the cycle that plays out in the second drama in the trilogy, The Libation Bearers.
in a tragedy peripetia is a sudden change of fortune for the tragic hero.