I recently flew Alitalia, but all the flights were Delta, so I checked in at Delta. However, there was a problem with my reservation (I was originally flying nonstop IAD-MXP on Alitalia, got rerouted IAD-ATL-MXP via Delta): the ticket number was never reissued. Since Alitalia originally issued the ticket, Delta could do nothing about it. So we waited on hold for hours, getting hung up on a couple times, trying to get the new ticket number. After a few missed flights we finally got one from Alitalia, and I was on my way...to VCE.