Axiom is reasonably easy to install using pip. However, it does require its dependency, Epsilon, during setup.py egg-info. That means that it needs to be available before pip tries to install Axiom. To make matters worse, Epsilon, in turn, requires Twisted to be available for setup.py egg-info.
In short, you need to do:
$ pip install Twisted
$ pip install Epsilon
$ pip install Axiom
Unfortunately, due to the way pip works, pip install Twisted Epsilon Axiom or putting both of them in a requirements file and installing it using pip -r does not work.