  The vacuum transition probabilities between to minima of a scalar field
potential in the presence of gravity are studied using the
Wentzel-Kramers-Brillouin approximation. First we propose a method to compute
these transition probabilities by solving the Wheeler-DeWitt equation in a
semi-classical approach for any model of superspace that contains terms of
squared as well as linear momenta in the Hamiltonian constraint generalizing in
this way previous results. Then we apply this method to compute the transition
probabilities for a Friedmann-Lemaitre-Robertson-Walker metric with positive
and null curvature and for the Bianchi III metric when the coordinates of
minisuperspace obey a Standard Uncertainty Principle and when a Generalized
Uncertainty Principle is taken into account. In all cases we compare the
results and found that the effect of considering a Generalized Uncertainty
Principle is that the probability is enhanced at first but it decays faster so
when the corresponding scale factor is big enough the probability is reduced.
We also consider the effect of anisotropy and compare the result of the Bianchi
III metric with the flat FLRW metric which corresponds to its isotropy limit
and comment the differences with previous works.
