Depth-one foliations, pseudo-Anosov flows and universal circles

Given a taut depth-one foliation \mathcal{F} in a closed atoroidal 3-manifold transverse to a pseudo-Anosov flow \phi without perfect fits, we show that the universal circle coming from leftmost sections associated to \mathcal{F} , constructed by Thurston and Calegari–Dunfield, is isomorphic to Fenley’s ideal boundary of the flow space associated to \phi with natural structure maps. As a corollary, we use a theorem of Barthelmé–Frankel–Mann to show that there is at most one pseudo-Anosov flow without perfect fits transverse to \mathcal{F} up to orbit equivalence.