No checked baggage means you are not going to check in your bag in the counter and Amtrak is not going to take and load your bag in train like they do on flight. You have to take it on the train and find a secure place for it in the overhead bins or under your sea. Amtrak allow you to carry a 50lb bag. Every car on Amtrak does have a spot on one of the end just for large baggage. You are good to go.
You'll be allowed to carry the baggage on the train. There is no area on the train for baggage. You'll hv to adjust it around your seating area.
You can take that on the train. Hopefully it fits in the overhead compartment or else you will have to put it by your seat
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