You can set runs to not be available for appointments.  Click on Calendar, Run Transfer.

Click on Run Transfer.

Double click on the run you'd like to mark as not available.

Choose the reason in the drop down then click on the calendar to choose the dates.

If you need to block off this run for more than one date, hold the Shift key on your keyboard while clicking on the dates.

Click Update when done.

Now that run will show as red and will not be available on appointments or to move pets to.