Syncing calendars across multiple shared booking pages

I have multiple shared booking pages where each appointment is with the same team. 

The set up I am trying to achieve is, if a customer books a time slot on one shared booking page this time slot is then removed across all other shared booking pages.

However, currently if a timeslot is booked on one shared booking page then the same timeslot shows as available and able to book on my other shared booking pages.