Catholics have been confused by modern theories about so-called and misapplied "material continuity". Just see how the CE explains it.
"Apostolicity is the mark by which the Church of today is recognized as identical with the Church founded by Jesus Christ upon the Apostles. It is of great importance because it is the surest indication of the true Church of Christ, it is most easily examined, and it virtually contains the other three marks, namely, Unity, Sanctity, and Catholicity ...
Apostolicity of mission is a guarantee of Apostolicity of doctrine. St. Irenæus (Adv. Haeres, IV, xxvi, n. 2) says: "Wherefore we must obey the priests [i.e. the Bishops; high priests] of the Church who have succession from the Apostles, as we have shown, who, together with succession in the episcopate, have received the certain mark of truth according to the will of the Father; all others, however, are to be suspected, who separated themselves from the principal succession" ... An authoritative mission to teach is absolutely necessary, a man-given mission is not authoritative. Hence any concept of Apostolicity that excludes authoritative union with the Apostolic mission robs the ministry of its Divine character.
Apostolicity, or Apostolic succession, then, means that the mission conferred by Jesus Christ upon the Apostles must pass from then to their legitimate successors, in an unbroken line, until the end of the world. This notion of Apostolicity is evolved from the words of Christ Himself, the practice of the Apostles, and the teaching of the Fathers and theologians of the Church ... Billuart (III, 306) concludes his remarks on Apostolicity in the words of St. Jerome: "We must abide in that Church, which was founded by the Apostles, and endures to this day.: Mazella (De Relig. et Eccl., 359), after speaking of Apostolic succession as an uninterrupted substitution of persons in the place of the Apostles, insists upon the necessity of jurisdiction or authoritative transmission, thus excluding the hypothesis that a new mission could ever be originated by anyone in the place of the mission bestowed by Christ and transmitted in the manner described ...
The history of the Catholic Church from St. Peter, the first Pontiff, to the present Head of the Church, is an evident proof of its Apostolicity ... Apostolicity is not found in any other Church. This is a necessary consequence of the unity of the Church. If there is but one true Church, and if the Catholic Church, as has just been shown, is Apostolic, the necessary inference is that no other Church is Apostolic."
http://www.newadvent.org/cathen/01648b.htm Hence, there is only one, easily discovered, Apostolic Church. And there alone you will find the Apostolic Hierarchy. And the Charism of Indefectibility in Catholic Doctrine is guaranteed there.
Here's the Truth: "material continuity" in the sense meant by modern sedeprivationists was historically applied by the Catholic Church to the Greek Orthodox Church. But the Greek Orthodox is a defected and schismatic Church that lacks Apostolicity. Hence, to try and apply the principles that were traditionally applied to the Greek Church to the Roman Church is nothing else than to say the Roman Church has defected and lost Apostolicity and become schismatic; all of which is simply impossible and a wrong application.
Don't shoot the messenger; but there it is