  We show that diffeomorphism invariance of the Maxwell and the Dirac-Hestenes
equations implies the equivalence among different universe models such that if
one has a linear connection with non-null torsion and/or curvature the others
have also. On the other hand local Lorentz invariance implies the surprising
equivalence among different universe models that have in general different
G-connections with different curvature and torsion tensors.
