  Quasigeodesic behavior of flow lines is a very useful property in the study
of Anosov flows. Not every Anosov flow in dimension three is quasigeodesic. In
fact up to orbit equivalence, the only previously known examples of
quasigeodesic Anosov flows were suspension flows. In this article, we prove
that a new class of examples are quasigeodesic. These are the first examples of
quasigeodesic Anosov flows on three manifolds that are neither Seifert, nor
solvable, nor hyperbolic. In general, it is very hard to show that a given flow
in quasigeodesic, and in this article we provide a new method to prove that an
Anosov flow is quasigeodesic.
