Improvements associated with the space that you occupy are non-deductible. However, improvements associated with common areas can be deductible (at least partially).
1) Repairs made on the personal side of the duplex cannot be deducted. It is a personal expense, just like your food expense.
2) Repairs made on the duplex are deductible against the rental income.
1) Improvements made on the personal side are added to the basis of the property, but you cannot depreciate the personal side of the property. The increase of the basis will help you minimize the taxable gain when you eventually sell the house.
2) Improvements made on the rented side will also be added to the basis, but you can depreciate the improvements on the rental side and deduct depreciation against the rental income. But, you have to recapture the depreciation (pay taxes again on what was deducted ) at the end when you sell the house.
So, a good strategy is:
A) For the personal side, do not do repairs because they are personal. Always do improvements because they increase your basis thus reduce taxable gain in the future.
B) For the rental side, do repairs because they are deductible right away and do not have to depreciate over few years as done for improvements. Repairs do not have to recapture when you sell the house too.