Apostolic Succession is the training of bishop's sucessor. One after another. It has nothing to with Peter according to the Eastern Orthodox.
Only that Peter was one of the Twelve who consecrated bishops during his lifetime, just like Paul did, through the imposition of his hands, which is part of the celebration of the sacrament of Holy Orders.
And you're right that Orthodox bishops are also valid bishops along with Catholic bishops, both the Catholic Church and the Orthodox churches validly celebrate the sacraments (I think they call them 'mysteries').
"Apostolic Succession" is a colloquial phrase that describes the sacrament of Holy Orders. Through the laying on of hands, the gift that Jesus gave to the apostles, including authority, is handed down from bishop to bishop.
Early Church historian J. N. D. Kelly, a Protestant, writes, “[W]here in practice was [the] apostolic testimony or tradition to be found? . . . The most obvious answer was that the apostles had committed it orally to the Church, where it had been handed down from generation to generation. . . . Unlike the alleged secret tradition of the Gnostics, it was entirely public and open, having been entrusted by the apostles to their successors, and by these in turn to those who followed them, and was visible in the Church for all who cared to look for it” (
Early Christian Doctrines, 37).
For the early Fathers, “the identity of the oral tradition with the original revelation is guaranteed by the unbroken succession of bishops in the great sees going back lineally to the apostles. . . . [A]n additional safeguard is supplied by the Holy Spirit, for the message committed was to the Church, and the Church is the home of the Spirit. Indeed, the Church’s bishops are . . . Spirit-endowed men who have been vouchsafed ‘an infallible charism of truth’” (ibid.).