There is not a way to 'gift' equity from one party to another unless both parties are related. Conforming lending guidelines will allow you to 'gift' equity from the seller to the buyer as long as there is a relation between the buyer and the seller. The specific rule follows the rules of any other gift on a conforming loan at that point. It states that the buyer must have at least 5% of their own funds for downpayment, unless the amount of the gift is at least 20%. If the amount of the gift (or gift of equity in this case) is 20% or greater of the sales price, no additional down payment is required.

As for verifying the relationship, that is up to the individual lender. Most will require some form of proof of relationship, as well as a signed affadavit prior to closing detailing the relationship between seller and buyer. Without this relationship, conforming guidelines don't allow for a gift of equity, and the purchase is then based off of the lower of the purchase price or appraised value, with no value being given to the 'gift of equity'.