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A general classical theorem is presented according to which all invariantrelations among the space time metric scalars, when turned into functions onthe Phase Space of full Pure Gravity (using the Canonical Equations of motion),become weakly vanishing functions of the Quadratic and Linear Constraints. Theimplication of this result is that (formal) Dirac consistency of the QuantumOperator Constraints (annihilating the wave Function) suffices to guaranteespace time covariance f the ensuing quantum theory: An ordering for eachinvariant relation will always exist such that the emanating operator has aneigenvalue identical to the classical value. The example of 2+1 QuantumCosmology is explicitly considered: The four possible ``CosmologicalSolutions'' --two for pure Einstein's equations plus two more when a $\Lambda$term is present- are exhibited and the corresponding models are quantized. Theinvariant relations describing the geometries are explicitly calculated andpromoted to operators whose eigenvalues are their corresponding classicalvalues.

SPACE TIME COVARIANCE OF CANONICAL QUANTIZATION OF GRAVITY: A (FORMAL) GENERAL RESULT AND THE (RIGOROUS) EXPLICIT CASE OF 2+1 QUANTUM COSMOLOGY