My gaming group is about to enter the 3rd Scenario: Blood Ties within short. My questions is regarding the investigators Equipment at the start of this scenario: do they get to keep any aquired spells, tomes, weapons or other equipent from Scenario #2?
You could certainly set aside the items they want to keep and let them start with them, if you want to. But I'd suggest adjusting the loot tiles on the new map accordingly; for each item you keep, one loot pile gets one less item card.
I would especially do this for unique items like spellbooks or arcane items.