  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.
