Can I use 7970 shifters (10spd DA) on a 6870 (11spd Ul) system and vice versa ?

I have 10speed 7970 on my tri bike.

I would like to move it to my road bike and buy 6870 for the tri bike.

If they are compatible, I will buy a 6870 road bike upgrade kit and put it on my tri bike, leaving my existing 7970 shifters

I will take the road shifters from the 6870 kit and put them on my road bike with the rest of the 7970 components


thanks