Hi @Reinhard1
You should have contacted Airbnb before canceling the reservation... you may be forgiven if this was an instant book... Try to contact them and ask...
You are the only responsible for your listing...You have an odd way to rent your place and prone to problems like this... the synchronization is about every 6-8 hours... So for every reservation you will be vulnerable to problems like this...
This mean even with the sync operating properly you may have problems... It happened to me when I had my listings in multiple websites... I got two reservations overlapping each other in about 10 minutes from each other...
On the only occasion my sync stopped I was warned via email and I took corrective action....
You can contact them via twitter @AirbnbHelp or phone...
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