Modern Vespa

Hello we are doing tires all the way around on our 2008 MP3 500.
We purchased the Michelin City Grips.
I took them to the shop to flip the tires. These tire are confusing as they are marked rear and a direction arrow. But also marked front with the opposite direction arrow.

At least they installed both the same direction. But they must have done one at a time because the "rear arrow" is pointing forward on both tires.
I think I can just flip the left and right wheel to change this but..

The tread on the grips look like they should only be a single direction. So what direction is best?
Not sure why the directions would be opposing for front and rear?
They will be doing the rear tire another day.
Thanks ahead of time

trust the arrows. arrow is the direction of rotation.

a tire with both arrows can be fitted front or rear so pay attention to which ever arrow is therefore appropriate.

on my gts looking from the front at the front tire the tread points upwards. looking at the rear tire from the rear the tread points upwards. ie opposite

Follow the arrows, it are this way as following where the pushing or braking power needs to grip.

This is the basic reason that tires that can be mounted forward or rear have arrows pointing in different directions, the rear tire are not designed for braking, but for pushing, the front ones are designed for braking, not pushing (we do not have 3x3 traction ).

So if rear is correct and fronts are inverted, swap the front tires (the advantage of two tires je je je) and you are in the good path.

Thanks everyone.
I will flip the tires left to right to get the front arrow facing forward. Sure is nice to have that trick up our sleeve !

Been doing a bunch of reading on opposing direction tread and I get it as far as the fronts do more braking than the rear so force is on the leading edge and the acceleration makes it wear the trailing edge on the rear.

I was questioning It because just didn't make sense to make the narrow part of the sipes ("v") point backwards and inward, I would have thought the open part of the "v" facing backwards would move water away instead I feel it directs water into the center are of the tread.
But they obviously know more about tires than me, I will "trust the arrows".