That AX psu has a max load of 1045w check here, and should operate at 900w very well, that's some serious headroom built in, real quality psu. It's all about the noise level once you go over 60% of the 850w.
Get the cards and a meter and try it, if it uses 750w or less keep it, if not change. obviously you cant get the 7990, so get the 7970 see how it goes if you fancy those cards.
Edit:
Just a thought I for some reason assumed your already got the psu If not then get something better.
Are you sure you want tri-fire? What res do you run at?
That wont run 2 7970s let alone a tri-fire setup.get 750 w corsair and be done
i thought 7xxx were less power hungry?
masscrazy it's a tough call, the AX850 really is nice, but most will tell you to play safe and get a higher rated psu.
The last resort (you seem set on this psu) is to get the AX850 with one card if the 7970 and test it overclocked hard, see what the power draw is and what headroom you have left. If it falls short then send it back within 7 days and replace it.
Looking at review for the 2 older cards the 6990 at full load including system pulls 434w and 137w idle, the 6970 pulls 340w full load and 161w idle.
The 6990 would pull 297w and the 6970 would pull 179w so this would be 476w with the GPU'S at stock so in theory you would be pulling 632w with the gpus at load.