  The vacuum transition probabilities for anisotropic universes in the presence
of a scalar field potential in the Wentzel-Kramers-Brillouin approximation are
studied. We follow the work by Cespedes et al [Phys. Rev. D 104, 026013
(2021)], which discuss these transitions in the isotropic context using the
Wheeler-DeWitt equation, the Lorentzian Hamiltonian approach and the thin wall
limit. First, we propose a general procedure to adapt their formalism to
compute the decay rates for any superspace model. Then we apply it to compute
the transition probabilities of an Friedmann-Lemaitre-Robertson-Walker (FLRW)
metric with both positive and zero curvature, reproducing in this way one of
the results obtained at Cespedes et al. We then proceed to apply the formalism
to three anisotropic metrics, namely, Kantowski-Sachs, Bianchi III and biaxial
Bianchi IX to compute the rate decays for these three cases. In the process we
find that this method involves some conditions which relates the effective
number of independent degrees of freedom resulting on all probabilities being
described with only two independent variables. For the Bianchi III metric, we
find that a general effect of anisotropy is to decrease the transition
probability as the degree of anisotropy is increased, having as the isotropic
limit the flat FLRW result.
