Contract says "and/or assigns" but the seller's agent crossed it out

You picked up on something real, and quarry named the reason. Equitable interest is the interest a buyer gets in a property the moment a valid purchase contract is signed, before closing and before title transfers. It's real, and it's what a wholesaler sells. It's also created by the contract, so the contract gets to say whether it can be handed to someone else. An initialed "buyer may not assign" is enforceable in most states, and assigning over it puts you in breach. Whether a court would treat it as a breach worth damages depends on state contract law, so a real answer on this specific paper needs a local attorney.

On "and/or assigns": it helps, but it isn't magic. Plenty of operators use a plain assignment clause spelled out in a paragraph instead, because a suffix on a signature line is easy for the other side to strike, as you just saw.

The part I'd think about harder is the agent. She struck that clause because she read you as someone who was going to resell her client's house at a markup, and now she's watching. If you go the double close route, where you actually buy the property and then sell it in a second transaction, that's two sets of closing costs, funding for a few hours or a few days, and in some states a transfer tax each way. On a house whose scope you already decided you don't want, that spread can shrink fast. Get the numbers on both closings before you pick a path.