That's a very good suggestion and it has been playing in my mind since the first possibility of synchronization in EasyList.

I'm sad to say that I currently don't have the knowledge to implement push technology.
But even if I had the knowledge I can foresee a few problems which needs to be solved:
- Currently synchronization overwrites the currently selected list. If it happened with a push message then it could overwrite a list you didn't want it to overwrite.
- If the app isn't running when the online list is updated then the push message wouldn't come through. I suspect that this can be solved by the next time you start the app to have it check for updates itself. Have a popup asking for permission to sync the items when a difference has been found.

This one needs investigation of a developer with the knowledge of push messaging to point me in the right direction.