  A pseudo-Anosov flow on a hyperbolic 3-manifold dynamically represents a face
F of the Thurston norm ball if the cone on F is dual to the cone spanned by
homology classes of closed orbits of the flow. Fried showed that for every
fibered face of the Thurston norm ball there is a unique, up to isotopy and
reparametrization, flow which dynamically represents the face. Using veering
triangulations we have found that there are non-fibered faces of the Thurston
norm ball which are dynamically represented by multiple topologically
inequivalent flows. This raises a question of how distinct flows representing
the same face are related.
  We define combinatorial mutations of veering triangulations along surfaces
that they carry. We give sufficient and necessary conditions for the mutant
triangulation to be veering. After appropriate Dehn filling these veering
mutations correspond to transforming one 3-manifold M with a pseudo-Anosov flow
transverse to an embedded surface S into another 3-manifold admitting a
pseudo-Anosov flow transverse to a surface homeomorphic to S. We show that a
non-fibered face of the Thurston norm ball can be dynamically represented by
two distinct flows that differ by a veering mutation.

Geometric Topology;Dynamical Systems