Your vase looks a little thin for neollitico, as they were heavily cased in clear glass. In the book Barovier by Marina Barovier, she describes neolitica glass as "an opaque mixture, resembling the texture of semi-prcious stone." I think the shape is wrong, too. Looking at the vase again, I think I was wrong in suggesting that it was twisted in an optic mould twice in opposite directions. I think it was twisted once and I'm seeing the rear of the vase through the front.
Here's a vase by Michael Worcester that was made in the way I described. It's hard to believe its not fenicio but I watched him make one.