Am I elegible for a TWOV?

I am flying from London to Shanghai and two days later to Taipei, then about a week after, I am back to Shanghai and stop only one night before leaving to London , do I surely qualify for a TWOV?
I wouldn't mind to save the 127Euros fee of the Visa but I also need to have peace of mind knowing that I will not. be refused entry or kept for long time to get a voa.I found surprising that the Chinese consulate in Rome, where I am at present, does not know this, hence nobody can confirm it to me in Italy, they suggested to contact Shanghai airport authorities!
Any certain source responding is very welcome > Thank you you in advance!