  An invariant description of Bianchi Homogeneous (B.H.) 3-spaces is presented,
by considering the action of the Automorphism Group on the configuration space
of the real, symmetric, positive definite, $3\times 3$ matrices. Thus, the
gauge degrees of freedom are removed and the remaining (gauge invariant)
degrees, are the --up to 3-- curvature invariants. An apparent discrepancy
between this Kinematics and the Quantum Hamiltonian Dynamics of the lower Class
A Bianchi Types, occurs due to the existence of the Outer Automorphism
Subgroup. This discrepancy is satisfactorily removed by exploiting the quantum
version of some classical integrals of motion (conditional symmetries) which
are recognized as corresponding to the Outer Automorphisms.
