  We compute transition amplitudes between two spin networks with dipole
graphs, using the Lorentzian EPRL model with up to two (non-simplicial)
vertices. We find power-law decreasing amplitudes in the large spin limit,
decreasing faster as the complexity of the foam increases. There are no
oscillations nor asymptotic Regge actions at the order considered, nonetheless
the amplitudes still induce non-trivial correlations. Spin correlations between
the two dipoles appear only when one internal face is present in the foam. We
compute them within a mini-superspace description, finding positive
correlations, decreasing in value with the Immirzi parameter. The paper also
provides an explicit guide to computing Lorentzian amplitudes using the
factorisation property of SL(2,C) Clebsch-Gordan coefficients in terms of SU(2)
ones. We discuss some of the difficulties of non-simplicial foams, and provide
a specific criterion to partially limit the proliferation of diagrams. We
systematically compare the results with the simplified EPRLs model, much faster
to evaluate, to learn evidence on when it provides reliable approximations of
the full amplitudes. Finally, we comment on implications of our results for the
physics of non-simplicial spin foams and their resummation.
