  A perturbative expansion of Loop Quantum Cosmological transitions amplitudes
of Bianchi I models is performed. Following the procedure outlined in [1,2] for
isotropic models, it is shown that the resulting expansion can be written in
the form of a series of amplitudes each with a fixed number of transitions
mimicking a spin foam expansion. This analogy is more complete than in the
isotropic case, since there are now the additional anisotropic degrees of
freedom which play the role of `colouring' of the spin foams. Furthermore, the
isotropic expansion is recovered by integrating out the anisotropies.
