  The system under study is the $\Lambda$-Kantowski-Sachs universe. Its
canonical quantization is provided based on a recently developed method: the
singular minisuperspace Lagrangian describing the system, is reduced to a
regular (by inserting into the dynamical equations the lapse dictated by the
quadratic constraint) possessing an explicit (though arbitrary) time
dependence; thus a time-covariant Schr\"{o}dinger equation arises.
Additionally, an invariant (under transformations $t=f(\tilde{t})$) decay
probability is defined and thus ``observers'' which correspond to different
gauge choices obtain, by default, the same results. The time of decay for a
Gaussian wave packet localized around the point $a=0$ (where $a$ the radial
scale factor) is calculated to be of the order $\sim
10^{-42}-10^{-41}\mathrm{s}$. The acquired value is near the end of the Planck
era (when comparing to a FLRW universe), during which the quantum effects are
most prominent. Some of the results are compared to those obtained by following
the well known canonical quantization of cosmological systems, i.e. the
solutions of the Wheeler-DeWitt equation.
