  We apply the ``consistent discretization'' technique to the Regge action for
(Euclidean and Lorentzian) general relativity in arbitrary number of
dimensions. The result is a well defined canonical theory that is free of
constraints and where the dynamics is implemented as a canonical
transformation. This provides a framework for the discussion of topology change
in canonical quantum gravity. In the Lorentzian case, the framework appears to
be naturally free of the ``spikes'' that plague traditional formulations. It
also provides a well defined recipe for determining the measure of the path
integral.
