Using both a Mac and a PC

I want to be able to sync/move a catalog between my PC and my Macbook Pro - both running Capture One Pro 9.

I have three computers running C1P 9. My main editing PC, my studio tethering PC and my traveling/location-tethering Macbook Pro.

I shoot tethered into both my studio PC and my location Macbook Pro. For this I use sessions initially, which are then moved into a catalog (with referenced images.

I do my editing on my home PC, as well as my Macbook Pro on the road (I do not edit on the studio PC)

The raw files are located on a separate disk on my home editing PC and copies are on an external drive attached to my Macbook Pro - this is easy to sync, as the raw files are always read-only.

The problem in this architecture seems to be syncing the catalogs between the home editing PC and the Macbook Pro (which I edit on while traveling). It seems the catalog can't be simply moved as the catalog is a different format (directories and such) on the PC and a file on the Mac. I was hoping to be able to simply copy between the two - now I'm thinking this paradigm I'm planning has some holes in it.

I want to use catalogs rather than sessions for my management for editing - Sessions although absolutely great for tethering (which I fully intend to continue with), are not so great when one has accumulated a lot of image assets.