Running remote mozilla

[moseley@hank.org]

I'm running mozilla on my laptop.  I wanted a bookmark on another machine so
I ssh to the other machine and run mozilla.  But instead of running the
remote version of mozilla I get a new window of my laptop's version of
mozilla.

In other words if I'm already running mozilla 1.0 locally and then run it on
another machine that has mozilla 1.3 I just get another window of my 1.0 
version.

But if it's not already running on my local machine I get version 1.3 from 
the remote machine.

I guess I wasn't expecting that.  But I suppose setting up the remote
DISPLAY gives the remote access to my locate screen (and all windows) so the 
remote mozilla can not only tell that's I have mozilla running but can also 
tell the local mozilla to create a new window.  Is that a close guess?

Is there a way so I can run both versions at the same time?

Thanks,