Warren, that is awesome! What an odd, nifty piece! I wonder if the bottom was suppose to hold something, like a centerpiece display of branches under the vase - or something.
Frank — Christine is doing far better than me — I've lost it completely. I had thought that casing and flashing were two different glassmaking techniques, not that they were differentiated by their purpose. Also that casing and flashing could take place inside an object. Also that gathering happened just the once. I can see that when the parison (hope that's correct) is returned to the pot for more metal (hope that's correct) to be added, I shall have to learn Italian to find out whether it's a second gather, being cased, or being flashed.
At least I have encalmo sorted out, 100% rock solid. Iestyn Davies explained it to me.
Bernard C. 
Bernard, you're right, they are different techniques (sort of). You can flash or case glass by dipping your object in glass, but flashing is a much thinner layer. Casing can also be done by cupping, in which one bubble is blown into a cup-shaped (bubble with an open end) piece of glass.
A parison (partially inflated gather, before it's been shaped) can be returned to the same pot for more metal, but at that stage it would probably be done to increase the thickness of part of it, or add something to the end. To be cased, I would think there would have to be a contrasting layer somewhere, but it could just be something like the opaque threads of Warren's vase.
Looks to me like the sides of a ribbed mold was lined with white rods, the pink blown into the mold, the vase then twisted and dipped (cased) in a layer of green.