Google too can track your Android phone I used it to get my stolen fone

Hey, guys, I was kind of curious about something, thought I might post it here.

For example, in the Bourne movies, and in many others, you saw Jason using prepaid phones in order to thwart those who might listen to his conversations. Now, instead of ditching the whole phone when they suspect it might be jeopardized, wouldn't it be possible for someone to remove the SIM, power the phone off, move to a different physical location, and then insert a different prepaid SIM, and thus have a "clean slate," as it were? Like starting with a new phone, since the new SIM has it's own identity.

Or is it possible for entities, such as the NSA, to track a phone by its IMEI number? Does that emit signal like the SIM that enable it to be tracked without a SIM, and make it possible for that phone to be identified consistently, even if a new SIM is used?

And if you power off/remove SIM, and then move, can you shake a triangulation? Or does it leave a "hook" in a triangulated phone? If you did this, would the process of tracing the phone have to be started all over again?

Thanks, guys. I may add to this, but that's it for now.