Is there any way to syncronize notifications between a Linux desktop and iOS?

I use notify-send and dunst for my notification system on my desktop. After a research, I found out that there are a few commercial solutions for sending push notifications to iOS devices, and I even wrote a script using Pushover. However, I did not find any way to get notifications from the iPhone displayed on my desktop. (Preferably using a unified notification system, for example using notify-send). I know that OSX has very good support for this, so I guess it's not impossible, but I did not find any working solution. Of course, the best solution would be to get full sync, including removing a notification from both places if it has been read in one place. A lot of this is already solved, of course. E-mail, Facebook, etc. notifications gets "synced" out-of-the-box basically. I'm ok with having to write scripts, including having to write customized filters, etc. If there's no full solutions, I'm satisfied with getting the building blocks only, especially something that sends the iOS notifications to my desktop somehow. EDIT: I added the tag Bluetooth because I learned that OSX does this using Bluetooth LE. Looking up Bluetooth LE support still did not help me, though.