We present a review of the relations between various equations for maximal
cut banana Feynman diagrams, i.e. amplitudes with propagators substituted with
δ-functions. We consider both equal and generic masses. There are three
types of equation to consider: those in coordinate space, their Fourier
transform and Picard-Fuchs equations originating from the parametric
representation. First, we review the properties of the corresponding
differential operators themselves, mainly their factorization properties at the
equal mass locus and their form at special values of the dimension. Then we
study the relation between the Fourier transform of the coordinate space
equations and the Picard-Fuchs equations and show that they are related by
factorization as well. The equations in question are the counterparts of the
Virasoro constraints in the much-better studied theory of eigenvalue matrix
models and are the first step towards building a full-fledged theory of Feynman
integrals, which will reveal their hidden integrable structure.Comment: 13 page