  We use parameterized Morse theory on the pages of an open book decomposition
to efficiently encode the contact topology in terms of a labelled graph on a
disjoint union of tori (one per binding component). This construction allows us
to generalize the notion of the front projection of a Legendrian knot from the
standard contact $\mathbb{R}^3$ to arbitrary closed contact $3$-manifolds. We
describe a complete set of moves on such front diagrams, extending the standard
Legendrian Reidemeister moves, and we give a combinatorial formula to compute
the Thurston-Bennequin number of a nullhomologous Legendrian knot from its
front projection.
