`cache`d folders are actually stored in S3, as I understand it, and restored on a per-branch basis (so every branch gets its own version of the cache).  For us, it looks like the folders are exactly as they were on the last build.

The `apt` one is a travis special flag meaning "keep track of any changes made by apt-get"-- specifically, it should only have to install `graphviz` once if this works.