Hi,
The "Select Shipment" page of Virtuemart doesn't work. Try to browser this page on your website:
www.atrezzointeriorisme.com/index.php?option=com_virtuemart&view=cart&tmpl=component&task=edit_shipment
it gives 500 Internal Server error. It is a Core Virtuemart page and has nothing to do with CleanMart. The "Select shipping" button on Cart page of CleanMart is just trying to load that page via AJAX loading. Since the page itself gives 500 internal server error, this causes infinite loading-time for AJAX loading because the page never gets loaded.
I suppose, one of the shipping plugin you are using is not compatible with the new Virtuemart version. (don't forget to update the Virtuemart AIO Component)
Try disabling the shipping plugins one-by one and each time browse this page:
www.atrezzointeriorisme.com/index.php?option=com_virtuemart&view=cart&tmpl=component&task=edit_shipment
Once you figure out the faulty plugin, completely disable or update it. Then everything will be good to go.
Cheers.