Wave interference is a such misnomer. There is no such thing as wave interference. On the contrary, the waves are passing each other without any distortion ( providing the medium through which the waves are traveling is elastic enough).
What we are calling interference is the wave traveling through medium which has been distorted by for example another wave.
Double slit experiment may indicate that there is a medium which is being distorted by photon or electron traveling through the other slit.
It would be very interesting to check the time distance between electron passing through one slit and electron through the other slit within which so called interference is still occuring.