You may transport rifles and firearms to the United States provided
you request permission from your airline during check-in.
Generally to transport your firearms, they must be unloaded and packed in a rigid face container. There are airlines that do not allow firearms even in checked baggage.
For the sight glasses, once separated and dismounted from the rifle
you have the right to bring them with you whether in checked
luggage or in cabin.
Before your flight to the United States, it is recommended that you read your airline's instructions and be well informed about firearms regulations. The law on weapons possession varies from State to State according to international transit laws.