nnoremap <Leader>b :buffers<CR>:buffer<Space>
nnoremap <Leader>n :bn<CR>
nnoremap <Leader>p :bp<CR>
So I'd give that a shot. If that doesn't work for you, try just ":tabe <file>" for your three files, then ctrl+pageup, ctrl+pagedown (or gt, gT) to quickly switch between them.
I just switched b/p (since I use p w/ ctrl-p as a fuzzy finder to list all files).