  We investigate the propagation of waves in one-dimensional systems with
L\'evy-type disorder. We perform a complete analysis of non-relativistic and
relativistic wave transmission submitted to potential barriers whose width,
separation or both follow L\'evy distributions characterized by an exponent $0
< \alpha <1$. For the first two cases, where one of the parameters is fixed,
non-relativistic and relativistic waves present anomalous localization,
$\langle T \rangle \propto L^{-\alpha}$. However, for the latter case, in which
both parameters follow a L\'evy distribution, non-relativistic and relativistic
waves present a transition between anomalous and standard localization as the
incidence energy increases relative to the barrier height. Moreover, we obtain
the localization diagram delimiting anomalous and standard localization
regimes, in terms of incidence angle and energy. Finally, we verify that
transmission fluctuations, characterized by its standard deviation, are
universal, independent of barrier architecture, wave equation type, incidence
energy and angle, further extending earlier studies on electronic localization.
