  Last years a certain attention was attracted to the statement that
Hamiltonian formulations of General Relativity, in which different
parametrizations of gravitational variables were used, may not be related by a
canonical transformation. The example was given by the Hamiltonian formulation
of Dirac and that of Arnowitt - Deser - Misner. It might witness for
non-equivalence of these formulations and the original (Lagrangian) formulation
of General Relativity. The problem is believed to be of importance since many
authors make use of various representations of gravitational field as a
starting point in searching a way to reconcile the theory of gravity with
quantum principles. It can be shown that the mentioned above conclusion about
non-equivalence of different Hamiltonian formulations is based on the
consideration of canonical transformations in phase space of physical degrees
of freedom only, while the transformations also involve gauge degrees of
freedom. We shall give a clear proof that Hamiltonian formulations
corresponding to different parametrizations of gravitational variables are
related by canonical transformations in extended phase space embracing gauge
degrees of freedom on an equal footing with physical ones. It will be
demonstrated for the full gravitational theory in a wide enough class of
parametrizations and gauge conditions.
