One bluetooth mouse for multiple windows in the same PC

I installed three windows 7 on my PC. Every time I switch from one to another, I have to unpair my bluetooth mouse and pair it again to use it, otherwise the mouse can not be found.

Is there any way to avoid unpairing/pairing for each time?

I did a website search. Most discussions focus on one mouse for multiple devices or two different OS in the same PC such as windows 7 and ubuntu. Multiple windows in the same PC are rarely discussed. I am not sure if the way they work are the same or not.