Hide links

Hi

This question is for a church organization website composed of The main Organization and 4 local churches. They are sharing the same member database thus the website will use a Multisite Subdomain install with 5 subdomains linked to their own domains. This should be as follow :

organization.org
church1.organization.org => linked to church1.org
church2.organization.org => linked to church2.org
church3.organization.org => linked to church3.org
church4.organization.org => linked to church4.org

Each website will show a static webpage with 5 buttons on the primary menu bar linked to the 4 other churches and the main organization.

So here is the question: is it possible to hide the link when a user goes from church1 website to church2 website so he doesn’t know that he is on another website ?

Let me explain in a schematic way :
When a user goes to church1.org and then on this page clicks on church2 button, he will see on his navigator bar something like church1.org/church2 and not church2.org so he think he is still on the same website he visited first.
Same if someone goes to church2 and then clicks on another church website.

Is it possible to hide the address ? This is my client request and i don’t know the feasibility of this feature.

Thank you guys for your time !