Thank you - you made me go back and look at what is in the admin and do a comparison with the published calendar. I always have my calendar set to Prep - None, so that's not the issue.
However I did noticed that for bookings made through Airbnb, the arrival and departure day is marked on the admin calendar but not on the published calendar, allowing it to be booked. BUT if you block off a booking yourself, made elsewhere, the whole day is marked off on the public calendar and cannot be booked.
I suppose the secret is when blocking off bookings yourself you should not include the arrival or departure day. Very fiddly and confusing. This is why syncing calendars doesn't work either....and why so many complaints. I don't sync calendars so it would have to be manual for me.
Still think that Airbnb should have changeover days as an option when blocking off as the system really only accommodates those that only take bookings through Airbnb and nowhere else.
Thanks again!