How would I know what immunity looks like? Police can and do lie to people to get them to confess to stuff. "We'll go easy on you, we promise", or "this is off

How would I know what immunity looks like? Police can and do lie to people to get them to confess to stuff. "We'll go easy on you, we promise", or "this is off the record, you can tell us anything now" etc. So what stops them from saying something like "sure, you got immunity, now let us in".