Connection between PCP and L=SL The book by Arora and Barak contains in chapter notes on PCP


  We note that Dinur's general strategy is somewhat reminiscent of the zig-zag construction of expander graphs and Reingold's deterministic logspace algorithm for undirected connectivity described in Chapter 20, which suggests that more connections are waiting to be made between these different areas of research. (pg 494)


What precisely is meant by this reminiscence? Is there a common property/lemma than can be "factored out" of these two proofs?
The precise answer to your question is given by Oded Goldreich in his article "Bravely, Moderately: A Common Theme in Four Recent Works".

Here is the link: http://www.wisdom.weizmann.ac.il/~oded/COL/brave.pdf