With artifacts, they work like this. Say you have the Battered Packet Of Spiced Cigarettes. At 0 Investigations, its Revelation is -1 DR to Stability tests. If you trade it to your buddy at the end of the investigation, you lose that benefit and they gain it instead. If your buddy carries the packet around for a whole investigation, they advance to the next Revelation (+1 Stability) but lose the benefits of the 0 Investigations Revelation (-1 DR to Stability tests.)
Basically, permanent effects like changes to Abilities and Hit Points and money stay with you even if you lose the artifact, but temporary effects like bonuses or penalties to DR or Social Standing or the Jeweler's Loupe's 0 Investigations Revelation don't.
Also you can definitely stack effects from artifacts.
The only thing you can't really do is indefinitely preserve a 0 Investigations Revelation by constantly swapping an artifact between owners. The investigator that used the artifact always advances to the next Revelation at the end of the investigation.
(This means that an investigator who carries the Battered Packet Of Spiced Cigarettes *will* get the +1 Stability Revelation, and this Stability increase will be permanent, even if they trade the cigarettes away at the end of the investigation. Also if they carry the packet around for *another* investigation, they'll get the -1 Stability Revelation, which will also be permanent, making their net Stability gain across all Revelations 0.)