The Continuity of the Bishops of Rome.
Saint Peter founded three Sees and the early Church placed them in this order:
Saint Peter went through all of these cities, and founded these three Sees. However, it was not until he died in Rome, that he was replaced with an immediate Successor (Saint Linus according to St. Irenaeus [Against Heresies 3:3.3]), whereas in the previous cities, he left a successor of that See, not a successor of himself, as he was still alive then. You cannot be completely replaced while you are still alive and fully representing yourself.
“The first see, therefore, is that of Peter the Apostle, that of the Roman church, which has neither stain nor blemish, nor anything like that. The second see is that of Alexandria, consecrated on behalf of the blessed Peter by Mark, his disciple and an Evangelist, who was sent to Egypt by the Apostle Peter, where he preached the word of truth and finished his glorious martyrdom. The third see is that of Antioch, which belonged to the most blessed Peter, where first he dwelled before he came to Rome, and where the name “Christians” was first applied, as to a new people.”
+ Decree of Damasus # 3, 382 A.D
A little Trivia & Facts:
St Peter (other named Simoen or Simon) was born on Bethsaida, Israel and died on Rome Italy and also the first Pope of the Catholic Church