Simultaneous universal circles

Let phi be a pseudo-Anosov flow on a closed oriented atoroidal 3-manifold M. We show that if F is any taut foliation almost transverse to phi, then the action of pi_1(M) on the boundary of the flow space, together with a natural collection of explicitly described monotone maps, defines a universal circle for F in the sense of Thurston and Calegari-Dunfield.