so I'll just begin.
Note that in the early/mid '90s there is an elevation in murder rate and, correspondingly an elevation in the manufacture and import of guns (ergo an increased availability).
The same pattern occurs in the 2012-2015 period. Increase in murder rate at the same time there is an increase in gun supply.
In the year preceding the 2014 sharp increase in murder rate/100,000 the import and manufacture of guns began, ergo more guns were available.
The number of guns available correlates to the murder rate. Showing causation is a bit more problematic; we can see that the trends are somewhat related but can't point to any one specific murder/mass shooting as a direct result of the increase in gun supply.
So, if there is a baseline of existing guns that corelates with a baseline in murder rate and an increase in gun supply that corelates with an increase in murder rate it seems to me that more guns means more murder.
I can speculate that the baseline of existing guns also corelates to a baseline of theft/loss/illegal sale guns and an increase in availability/supply will corelate to more guns in the illegal market.
I admit that I'm not a statistician and am not educated in that field, however it seems to me that if there are more cars on a freeway there will be more accidents.