  A systematic analysis of the symmetries of topological 3D gravity with
torsion and a cosmological term, in the first order formalism, has been
performed in details - both in the hamiltonian and lagrangian formalisms. This
illuminates the connection between the symmetries of curved spacetime
(diffeomorphisms plus local Lorentz transformations) with the Poincare gauge
transformations. The Poincare gauge symmetries of the action are shown to be
inequivalent to its gauge symmetries. Finally, the complete analysis is
compared with the metric formulation where the diffeomorphism symmetry is shown
to be equivalent to the gauge symmetry.
