Over the life of this series from 1953 to 1976, two watermarks were used - winged wheel and multiple stars.
Simple right? That was my happy state at the time of the original post; now it's a question of how deep to go into this quite complex set.
Let's start with the winged wheel watermark - a wheel with a wing on top. First complication is that there are three sizes of this - Types I, II and III

Next complication - imagine that the paper company has delivered an order of one of these types to the Italian Post Office Printing company. Because it is an asymmetric watermark, the young apprentice there could feed the paper into the printing machine in 8 different ways. I was initially confused by references in the buy/sell sites to watermark codes like ND and NS. It turns out you only need to learn 6 words of Italian to make sense of this.
N - Normale - Upright
C - Capovolta - Inverted
S - Sinistra - Left
D - Destra - Right
A - Alto - Up
B - Basso - Down
Sure enough there are 8 possible combinations of these
NS and ND - Upright with Wing Tip to Left and Right

CS and CD - Inverted with Wing Tip to Left and Right

SA and DA - Left and Right with Wing Tip Up

and finally SB and DB - Left and Right with Wing Tip Down

So I thought, now all I have to do is quickly identify the ones in my collection based on this result. Problem! Most times the watermark is at the edge of the stamp so I cannot determine Type I, II or III. I imagine an Italian dealer could do this in his sleep but not me.
Without a specialty catalogue I also don't know if these Syracusas come in all watermark types and orientations.
Isn't this the great thing about worldwide collecting of the common stuff though - I now need to hunt for not just a nicely postmarked front side but also with a nicely centered watermark on the back. Maybe such a collection would not be so common after all?
I will have a go at the multiple stars watermark in a future, separate post.
Final scary thought; two other very common series - the 1945-47 Breaking Chain/Planting Tree/Torch/etc. (Scott 463 - 476) and the 1950 Occupation series (Scott 549 - 565)have this Winged Wheel watermark. Do they come in all these possible permutations of type and orientation? I may have a go at those one day.