Is OMW sharing each environments?

Hi, I was wondering if OMW is sharing each environments like DV, PY, PD with its objects?  Meaning that regardless of what environment user login, they will be using same objects between all environment?

I noticed from the project advancement, the object will be transfered from one to another..is that correct ? Eg, DV to PY then to PD

pls kindly clarify

thanks,