Reonomic homogenious contact transformations and path reparametrization in path integrals over quasi-measures

In path integrals over quasi-measures for linear parabolic fourth order differential equations with the explicit dependence of coefficients on time the reonomic homogeneous contact transformations and path reparametrizations are considered. An integral relation between Green's functions for the fourth order differential equations being in correspondence is found. Differential operator of the transformed equation coincides in the particular case with the conformally covariant Bol operator, that is well-known in exactly solvable and conformal models.