Busts / heads right or left is not a really big deal, except for the catalog numbers.
When a new emperor came to power, multiple plaster busts or heads were made of him, and dispatched to the various mints around the Empire with expediency.
I this way, the coin engravers could be all 'on the same page', (so to speak), and those mints can be differentiated by the slight variations in style that would be characteristic to a particular Mint.
The most experienced engravers would then engrave the heads / busts on the dies, and the less experienced or talented engravers would put the legends on the dies in mirror reverse.
The same sort of thing would happen with the effigies.
When a new emperor came to power, multiple plaster busts or heads were made of him, and dispatched to the various mints around the Empire with expediency.
I this way, the coin engravers could be all 'on the same page', (so to speak), and those mints can be differentiated by the slight variations in style that would be characteristic to a particular Mint.
The most experienced engravers would then engrave the heads / busts on the dies, and the less experienced or talented engravers would put the legends on the dies in mirror reverse.
The same sort of thing would happen with the effigies.