The spatial distribution of the incompressible edge states (IES) is obtained for a geometry which is topologically equivalent to an electronic Mach-Zehnder interferometer, taking into account the electron-electron interactions within a Hartree type self-consistent model. The magnetic field dependence of these IES is investigated and it is found that an interference pattern may be observed if two IES merge or come very close, near the quantum point contacts. Our calculations demonstrate that, being in a quantized Hall plateau does not guarantee observing the interference behavior.