flying in from taipei to hk to china and back to taipei

Hello,
would you please be able to answer me this question.

I was thinking about flying from Taiwan to Hongkong then going to China. There I would apply for the 72hours visa and fly back to Taiwan.

Does it work if I buy 3 flight tickets (Taiwan-Hongkong, Hongkong-china, China-Taiwan) lets say from different carriers, or does it have to be one carrier? I am a bit confused that transit actually means, since I used to have only a 4hour-6hour transit, never 3 days.

Thank you very much