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Based upon the exact formal solutions of the Weyl-Dirac-equation inanisotropic planar Bianchi-type-I background spacetimes with power law scalefactors, one can introduce suitable equivalence classes of the solutions ofthese models. The associated background spacetimes are characterized by twoparameters. It is shown that the exact solutions of all models of a givenequivalence class can be generated with the help of a special transformation ofthese two parameters, provided one knows a single exact solution of anarbitrary member of this class.  The method can also be utilized to derive approximate solutions, i.e.solutions which exhibit the correct behavior at early and at late times aswell. This is explicitly demonstrated for the case of the anisotropic Kasnerbackground with axial symmetry.

Massless Fermions in planar Bianchi type I universes: Exact and approximate solutions