  In this paper we consider vacuum Kasner spacetimes, focusing on those that
can be parametrized as linear perturbations of the special Petrov type D case.
For these quasi-D Kasner models we first investigate the modification to the
principal null directions, then a Teukolsky Master Equation for fields of any
spin, considering in particular the quasi-D models as curvature perturbations
of the type D background. Considering the speciality index and the principal
null directions and comparing the results for the exact solutions and those for
the perturbative ones, this simple Kasner example allows us to clarify that
perturbed spacetime do not retain in general the speciality character of the
background. There are four distinct principal null directions, although they
are not necessarily first order perturbations of the background principal null
directions, as our example of the quasi-D Kasner models shows.
  For the quasi-D Kasner models the use of a Teukolsky Master Equation, a
classical tool for studying black hole perturbations, allows us to show, from a
completely new point of view, the well known absence of gravitational waves in
Kasner spacetimes. This result, used together with an explicit expression of
the electric Weyl tensor in terms of Weyl scalars, provides an example of the
fact that the presence of transverse curvature terms does not necessarily imply
the presence of gravitational waves.
