An Anosov flow Φ on a closed 3-manifold M gives rise to a non-Weinstein Liouville structure on V:=[−1,1]×M. Building upon the work of Hozoori, we establish a homotopy correspondence between Anosov flows and certain pairs of contact forms. Moreover, the symplectic invariants of V only depend on the \emph{homotopy class of Φ}. We focus on a subcategory 0 of the wrapped Fukaya category of V whose objects are in bijection with the simple closed orbits of Φ. In contrast with the Weinstein case, 0 is \emph{not homologically smooth}, as it is not finitely split-generated in a maximal way. We expect 0 to be a powerful new invariant of Anosov flows. This talk is partly based on joint work with Oleg Lazarev and Agustin Moreno.