What do you call those braided door coverings I saw all throughout Umbria and Tuscany

I think you are talking about the "tende antimosche", to keep the flies out? Enter "tende antimosche" on google Image search and see if that is what you meant.

In English they are called insect blinds or fly blinds. Do a search on line. They have in on Pintinterest and other sites.

Are these the same as the colorful hangings in doorways on Burano?

Roberto, thank you for your reply. You are correct -- this is exactly what I meant. Now, the grand mission to find a supplier for the US :-)
Appreciate your time, and this forum. It was a great help.

I love those too. I started hanging sheer net type curtains (from Ikea)as a type of screen door a number of years ago after seeing those in Italy. The neighbors think i am a kook!
I think it would be easy to make if you found the appropriate type of cording... I will have to take a look on pinterest.

Edit... just found the exact ones on sale at Ikea... it kind of looks like chenille cording.

Now, the grand mission to find a supplier for the US :-)

there are some neat things you can see traveling that just aren't available here. Ever since first seeing them I thought I could make a fortune if I could become the US importer for this type of shutter! You can swing it all the way open like a regular shutter, but when the sun is blazing you can crank up the hinged part so you still get a breeze but block the sun from the interior. https://s-media-cache-ak0.pinimg.com/564x/95/30/6f/95306fc0dafc6d166a734fdf7e3a0607.jpg

No John. It's not that easy as it looks. The way houses are made in America makes it difficult to install those shutters, that is way when you see them around here, they are fake shutters basically painted on the wall open.

The problem is that in America often the window panes are mounted flush with the exterior of the wall and there is no window sill on the exterior.

As you can see in the picture below, therefore the shutters are basically just a fake design (like in the same picture) because the outside shutters would interfere with the window pane:
https://s-media-cache-ak0.pinimg.com/originals/60/c3/1e/60c31e91ab3951d7e657718a79c57c74.jpg
https://i.ytimg.com/vi/_r-YK2anhVo/maxresdefault.jpg

In Italy the windows pane in the casements are mounted flush with the interior of the wall, and the window sill is on the outside. Therefore there is room for the shutters, as you can see in the picture below:
http://www.finartserramenti.it/wp-content/gallery/persiane-alluminio-starwood/Persiana-1.jpg

So in America they have to mount them somewhat differently:
https://www.tucsonrollingshutters.com/wp-content/gallery/rolling-shutters/stucco-lb-shutter.jpg
https://s-media-cache-ak0.pinimg.com/236x/dd/34/51/dd34516bbec78ec7e0f273f45240c408.jpg

Roberto, thanks for the explanation! Guess I'm not going to become rich as the shutter king. Better stick to buying lottery tickets.

I know, i love those shutters too, you can move each panel to any position, and then fix the bottom hinges to let fresh air in and keep the storm out! Ingenious!
Here we have to close up everything in a storm, and that's the best time to get fresh air circulating! How Dumb is that!