Almost commensurability of 3-dimensional Anosov flows

Two flows are almost commensurable if, up to removing finitely many periodic orbits and taking finite coverings, they are topologically equivalent. We prove that all suspensions of automorphisms of the 2-dimensional torus and all geodesic flows on unit tangent bundles to hyperbolic 2-orbifolds are pairwise almost commensurable. The proof relies in particular on the existence of some specific genus one Birhoff sections for geodesic flows, a construction that we will explain.