No, if you have already deducted the new water heater as an expense 3 years ago you will not add it to the basis of your property.
The basis you reference in your sentence, "The cost (basis) of an asset is the amount you paid for it plus what you spent to acquire the item, such as freight, installation, sales tax, and legal fees) I guess it confuses me", refers to the starting basis to which you would add any capital improvements which would give you the adjusted basis used to calculate any gain or loss.
@sand1tiger
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