How to keep close a sub-menu under homepage? [closed]

To do that, you have to set hidden attribute to the sub menu.

CSS

#wrapper .fusion-vertical-menu-widget.left .menu .sub-menu {
    display: none;
}

to toggle display on the menu on hover over servizi, you can add jQuery hover to the menu item.

jQuery

var subMenu = jQuery("#wrapper .fusion-vertical-menu-widget.left .menu .sub-menu");

jQuery("#menu-item-12049").hover(function(){
   subMenu.show();
  }, function(){
   subMenu.hide();
});

Note: You should change the class values to more appropriate values, these are just extracted from what I saw, but probably a good idea to get better css selectors