  Based upon the exact formal solutions of the Weyl-Dirac-equation in
anisotropic planar Bianchi-type-I background spacetimes with power law scale
factors, one can introduce suitable equivalence classes of the solutions of
these models. The associated background spacetimes are characterized by two
parameters. It is shown that the exact solutions of all models of a given
equivalence class can be generated with the help of a special transformation of
these two parameters, provided one knows a single exact solution of an
arbitrary 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 as
well. This is explicitly demonstrated for the case of the anisotropic Kasner
background with axial symmetry.
