Transit at more than one Chinese airport, require visa or stopover permit?

I am an Australian citizen travelling on Australian Passport. Have a return flight from Sydney Australia to Rome Italy. On the way there are connecting flights in China as follows....

Outbound flight is Sydney to Beijing to Rome.

Inbound/Return flight is Rome to Beijing airport to Shanghai airport then to Sydney.

I fly with Air China the whole way. Can anyone who knows about this please advise if I will require any visas while transiting in China, in particular the return flight where I have to go from Rome to Beijing airport then to Shaghai airport before finally to Sydney?

Many thanks.