  Starting from an action for discretized gravity we derive a canonical
formalism that exactly reproduces the dynamics and (broken) symmetries of the
covariant formalism. For linearized Regge calculus on a flat background --
which exhibits exact gauge symmetries -- we derive local and first class
constraints for arbitrary triangulated Cauchy surfaces. These constraints have
a clear geometric interpretation and are a first step towards obtaining
anomaly--free constraint algebras for canonical lattice gravity. Taking higher
order dynamics into account the symmetries of the action are broken. This
results in consistency conditions on the background gauge parameters arising
from the lowest non--linear equations of motion. In the canonical framework the
constraints to quadratic order turn out to depend on the background gauge
parameters and are therefore pseudo constraints. These considerations are
important for connecting path integral and canonical quantizations of gravity,
in particular if one attempts a perturbative expansion.
