Our following itinery. Can we get a Visa Free Transit?

Fly from UK on 2.7.18 at 16.20pm
Land in Beijing 3.7.18 at 09.30am.
Capital Intl Airport.

Fly from Beijing 4.7.18 at 21.15pm
Land in Xian 4.7.18 at 23.25pm.
Xianyang Intl Airport.

Fly from Xian 5.7.18 at 21.45
Land in Chengdu 5.7.18 at 23.20.
Shuangliu Intl Airport.

Fly from Chengdu 8.7.18 at 21.45
Land in Australia 9.7.18 at 10.25am.

We calculate 132hrs & 15 mins but not sure if the cities are included in the Visa Free Transit?

Thank you in advance.