Halliday & Matthiessen (2014: 333n):
Note that ‘transitivity’ is the name for the whole system, including both the ‘transitive’ model and the ‘ergative’ one. ‘Ergativity’ is thus not the name of a system, but a property of the system of transitivity: within this system of transitivity, we can recognise the ‘transitive model’ and the ‘ergative model’.