  Any closed, oriented, hyperbolic three-manifold with nontrivial second
homology has many quasigeodesic flows, where quasigeodesic means that flow
lines are uniformly efficient in measuring distance in relative homotopy
classes. The flows are pseudo-Anosov flows which are almost transverse to
finite depth foliations in the manifold. The main tool is the use of a sutured
manifold hierarchy which has good geometric properties.
