wave, waver, waive, waiver
Wave (noun or verb) refers to a movement of the hand in greeting or signal, or to an item moving to and fro. You can wave your hand. You can wave a flag. There are also waves in the sea, and sound waves and so on. The word wave can also mean a sudden occurrence of or increase in a phenomenon, as in the second or third wave of Covid.
To waver means to be undecided or to quiver or flicker like a flame. A waver could also be a person who waves, I suppose.
When you waive something, or agree to a waiver, this means that you give up your right or refrain from demanding compliance. Some vehicle rental companies operate an optional CDW (collision damage waiver) which you can opt out of at your peril.
I have before me a service contract which tells me, “If You experience the same fault again within 14 days, any Fixed Fees/ Excess applicable will be wavered.” They mean waived. (Unless they’re trying to tell me that they would remain undecided as to whether to charge an excess again.)
And I read in a news article: “We know that any deal will be waived through by virtually all opposition parties.” The author meant “waved through” (even though the opposition parties might be waiving their right to vote against the motion).
You can read about the difference between wave and waive and a whole lot more, in the English Digital Content style guide.