The pics aren't too sharp, but I'll take a stab at it. run Model 1870/87/15 Italian Vetterli through your favorite search engine for the history narrative. Long story short, an 1870/87 Italian Vett in 10.4x47R caliber was converted to 6,5x52 caliber in the dark days of WW1. Mostly used by other than front line troops.
I really can't tell anything from your pics, but standard on the stock are the conversion to Vitali magazine system cartouche and the conversion to 6.5 caliber cartouche. The latter is often 8-sided and shows the work was done at the arsenal in Rome.
The top barrel flat normally ( but not always) shows PP in script which indicate the Italian words for 'interchangeable parts' Also found there are various refurb and armorer's marks. Left side barrel flat shows the year the rifle was actually made, and right side barrel flat shows the serial number.
It looks like there are multiple serial numbers on the stock. If so, it's a force match from refurb.
I'd like to do better, but I'm just not picking up much detail from the pics. SW