What is the peripeteia that happens simultaneously with Oedipus's anagnorisis?

When Laius hears the prophecy that foretells he will be murdered by his own child and that this son of his would bed his mother he is so determined to make sure it doesn’t come true that he actually has a shepherd of his take his son out to the mountains with the intent of leaving him there to die. The shepherd could not bear to let the baby die, so he gave him to another shepherd from another kingdom. This shepherd brought the baby to the king and queen of that kingdom to raise as their own, since they could not have children. Later, another prophet predicted to that baby, which was Oedipus that he would murder his father and bed his mother and he tried to avoid this by leaving his adopted kingdom, unaware that these were not his birth parents.

i think this is the answer to your queston.