If you're worried about safety of those bulges don't. Pedersoli uses really good steel (30CrMo4/EN 1.7216). Supposedly same type of steel as was used for German machine gun barrels in WW2.
They already replied the gun is safe to shoot.
The below is for people like me interested in verifying it for themselves
The way all steels break is by elongation. One can roughly estimate if a given steel has reached close to its breaking point by comparing actual deformation with maximum elongation for this type of steel given in tables. This particular steel comes in two varieties. Tempered or annealed. As not many people can measure Brinell hardness at home when estimating safety we have to assume the worse of the two. Tempered is much stronger but its elongation at break is only 12%, Annealed is weaker, but it can elongate to 23%. We can't simply measure the bulge and if the resulting diameter is less than 112% of the normal call it good, because within the bulge itself there are areas where steel elongated more than others. However, if we measure the bulge (outside) and the diameter increase is let's say 3% bigger. At the same time there are no cracks at all. I would consider it safe and shoot it myself.
If it patterns well just shoot it.
Regarding steel shot. Many Pedersoli SxS (like mine) have chrome lined barrels. I don't know when exactly they started doing that. If your gun has chromed barrels steel shot is fine. To find out if you can't tell by looking, or test the surface (by using bluing liquid) best to write Pedersoli with the serial number.
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