How to tell a neighbor is away

One of the big things in Greece (moreso in the bigger cities) is the propensity for takeout places to send people to all the apartment buildings and put flyers under everyone's door. Somehow this manages to happen even though usually the entrance doors to the building are locked, because people just buzz anyone in sometimes. I imagine the conversation goes something like this:

"Bzzzzzzzz!"
"Yes?" (ok, I'm not doing this in Greeklish)
"I'd like to litter your hallways with flyers"
Now comes the low humming sound of the locking mechanism being released, and in comes flyer man into the building.

Of course, this doesn't apply to our building, because someone decided that our entrance door would stay open all the time.

Overall, I don't mind getting flyers from takeout places, because hey, this American Greek household is all about ordering out (even though my mother-in-law thinks I cook every day, can I say that one more time???). But the problem is, they don't always subtlely fling them under people's doors. They drop piles of them in the hallway, sometimes leaving a bread crumb trail of flyers leading from the front door to the elevator. It seems our neighbor across the hall is either away, or no longer inhabits the apartment. He still has his nice little name plate on the front door, so I assume he still owns the flat. Or maybe it is the name of the last tenant. (Yes, yes, I've said before how nosey I am about my neighbors) At any rate, he has a pile of flyers lying half inside/half outside his door, and they keep accumulating daily. And it is because they are half inside that noone can clean this crap up. We had the same issue with an uninhabited apartment next door to us in Athens, the paper just accumulated so much I don't think flyer man could push any more under the door.

I think what I might do is just push them so they are fully under his door, but I'm too afraid of getting caught. With only one other apartment on my floor who is going to catch me? I'm so chicken. Ah well, let the flyers accumulate if they will. Mr. Neighborman will have fun picking them all up if he ever comes back to his apartment.