The interaction between two edge dislocations in the presence of a tilted lens is studied. It is shown that for the interaction between two off-axis edge dislocations, the edge dislocations vanish, and one or two noncanonical vortices appear under certain conditions. A noncanonical vortex appears for the interaction between the on-axis edge dislocation and off-axis edge dislocation. However, one or two edge dislocations may take place when two edge dislocations are perpendicular or parallel to each other in the initial plane. The variation of the tilt coefficient does not affect the type and number of phase singularities, but the relation between the transverse position of phase singularities and the tilt coefficient is linear. The three-dimensional trajectories of vortices are nonlinear while the center of the pair of vortices propagates along a line during propagation.