Anosov flows are important examples of dynamical systems because of their stability. I will explain some joint work with Jonathan Bowden in which we answer an old question from Kirby's problem list about the abundance of these flows: given some number N, can you always construct a hyperbolic 3-manifold which supports N inequivalent skew-Anosov flows?
Most of the talk will be devoted to explaining classical background: examples of Anosov flows, surgery arguments to build new flows from old ones (following Handel and Thurston), some theory of hyperbolic Dehn filling, and pictures of the ingredients in our proof.