Skewed Anosov flows are orbit equivalent to Reeb-Anosov flows in dimension 3

We prove that in dimension 3, Anosov flows which are $\mathbb{R}$-covered and skewed are orbit equivalent to Reeb-Anosov flows. We characterize the existence of an invariant contact form or of a Birkhoff section with a given boundary, in terms of linking numbers between two invariant signed measures. Furthermore, we prove the existence of open book decompositions with one boundary component for Reeb-Anosov flows.