  Einstein-Weyl structures on a three-dimensional manifold $M$ is given by a
system $E$ of PDEs on sections of a bundle over $M$. This system is invariant
under the Lie pseudogroup $G$ of local diffeomorphisms on $M$. Two
Einstein-Weyl structures are locally equivalent if there exists a local
diffeomorphism taking one to the other. Our goal is to describe the quotient
equation $E/G$ whose solutions correspond to nonequivalent Einstein-Weyl
structures. The approach uses symmetries of the Manakov-Santini integrable
system and the action of the corresponding Lie pseudogroup.
