Equality Etiquette

You have two integers $A$ and $B$, and you'd like to make them equal. To this end, you can perform several moves. On the $i$-th move, - If $i$ is odd, either add $i$ to $A$ or add $i$ to $B$. Note that you aren't allowed to add $i$ to both, and must choose exactly one of them. - If $i$ is even, either subtract $i$ from $A$ or subtract $i$ from $B$. Once again, you aren't allowed to subtract