Here are some notes from my Ecclesiology class, where we discussed in detail the ecclesiology of the RC and the OC, etc. The quote is a direct quotation from Fr. Emannuel Clapsis, our professor.
"The bishop, in moments of crisis, when the communion is threatened by schism or other matters, the churches come into council not to verify the catholicity but to verify the presuppositions of their communion, to reaffirm them. So, a decision of the council must be received by the multiple local churches to be abiding and authentic and normative for their lives. For us the universal church is manifested in the local. In the universal ecclesiology of RC, there is one church, the church of Rome and all the other local churches are parts of this local church. Therefore none of them is the fullness of the church, but all of them together, under the Pope, constitutes the one, holy, catholic and apostolic church.
Because of the qualitative nature of the local church, every local church is the one, holy, catholic and apostolic church. But these local churches have the right faith, are celebrating the Eucharist under the presidency of the bishop and therefore they are JC himself and are in communion with each other and their communion is of identity and not of administrative or juridical structures. So for OC the local church is the manifestation of the one holy catholic and apostolic church. Each local church is the manifestation of JC by virtue of its celebration of the eucharist and there is no eucharist w/o the bishop."