How make multiple directories appear as one to a user on linux?
You can use UnionFS that seems to be actively developed or in case of the directories being separated hard drives, MHDDFS, but I see less references to that last one.
EDIT: There's an wikipedia article with more palatable info on UnionFS
If the directory contents are mostly static, you might achieve that with symbolic links, i.e. symlinking every file present in each of the three directories to a fourth one.