How much historical evidence do we have for some of the claims Eastern Orthodoxy typically makes?

by yarbousaj

I've heard that Eastern Orthodoxy is able to directly trace back things, namely apostolic succession and church traditions, from today all the way back to the original apostles when Jesus was alive. How much evidence, if any, is there for such a claim?

Note: I'm not asking about whether Jesus actually existed, the accuracy of the Bible, etc. There are a bunch of good posts in the FAQs dealing with those, for anyone curious.

zophister

Isn't apostolic succession a Catholic claim as well? It seems both churches would claim the same names for the first thousand-odd years, is this the case, and can these claims be similarly tracked down?