I would like to see my Calendly availability slots in my Google Calendar

At present I have to create new events in my calendar to show what availability I have given in Calendly, because the slots I have given as available in Calendly do not appear in my linked Google Calendar. Only booked appointments appear in my Google Calendar.
This means that in order to avoid clashes I have to manually update my own calendar every time I update my availability in Calendly. 
Could there be two different types of events that are sent to the linked Google Calendar: available slots and booked meetings?