How do the Blutsauger's and the Amputator's passive health regeneration modifiers stack?

• The Medic, by default, passively regenerates +3 health per second.
• The Blutsauger decreases this: –2 health per second.
• When active, the Amputator increases this by +3 health per second.

Now, I usually have both the Blutsauger and the Amputator equipped at the same time, meaning that my passive health regeneration should be +4 per second with the Amputator active, and +1 per second otherwise.

However, in reality, I notice that, sometimes, if I switch to the Amputator and then switch back to my Blutsauger, I will passively regenerate +4 health per second (despite the fact that the Blutsauger is the active weapon, and not the Amputator). Even stranger, I sometimes regenerate +6 health per second when the Amputator is active (as if I didn't have the Blutsauger equipped).

This begs the question: what are the criteria for the Blutsauger's –2 passive health regeneration per second (i.e. does it have to be active in order for this effect to apply), and, similarly, what are the criteria for the Amputator's +3 health regeneration per second?