Transitive Anosov flows on non-compact manifolds

In this article we study topological transitivity of Anosov flows on non-compact 3-manifolds. We provide both homological and homotopical conditions under which lifts to infinite covers of transitive Anosov flows stay transitive. In particular, we show that most transitive Anosov flows admit a transitive lift to an infinite cover, and we build a family of examples of transitive Anosov flows on non-compact manifolds that satisfy a homotopical characterization of suspension flows.