  We introduce a new method of constructing Birkhoff sections for pseudo-Anosov
flows, which uses the connection between pseudo-Anosov flows and veering
triangulations. This method allows for explicit constructions, as well as
control over the Birkhoff section in terms of its Euler characteristic and the
complexity of the boundary orbits. In particular, we show that any transitive
pseudo-Anosov flow has a Birkhoff section with two boundary components.
