Hi, I've found this photo of my grandfather, dated 1929, during a training camp; he holds a strange rifle, something like a carbine, possibly a small/reduced version of the Carcano. What is your thought?

I think it is a Carbine M1891 TS. Reference Small Arms of The World 12th edition page 577.

looks like the 91 most carcanos had short bbls 20" i had one like it, same thing oswald used 6.5 caliber( actually .268)
the ones w/ folding bayonet had 17" bbls