Be careful, the two transactions are entirely separate. Any additions to the cost basis of the new home won't have any tax effect until you sell that home in the future. Keep records as long as you own the home, but improvements to home #2 don't change the capital gains tax owed on the sale of home #1.
Also, not all the items you mentioned will be adjustments to cost basis. You can include improvements, but not repairs. Repairs maintain the property in as-is condition and can't be added to your basis. Improvements (or betterments) make the property more valuable or extend the useful life of the property or its subsystems. Improvements must also be permanently attached to the real property (the land, or anything permanently attached to the land). Furnace repair is not a cost basis adjustment, but replacement would be (because it extends the useful life of the heating and cooling system). Replacing a built-in cooktop would be an improvement because it is built-in, but costs for freestanding appliances are not counted as cost basis adjustments. Patching the roof is a repair, but replacing the entire roof (or a substantial section) that gives it a new 15 year life cycle would be an improvement. And so on.
