How do you transfer checked baggage when flying multiple carriers?

Can you answer robgs1783’s question about Luggage?:

And, without have to go to the baggage claim and then back through secruity and the ticketing counter of the different carrier.
ie. If I fly United into JFK, and am flying Jetblue from JFK to LAX, and I have an hour layover, how do I transfer my bags without them going down to the baggage claim and then having to check them again???

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What is the process to get my checked luggage from one carrier to another when I have a layover?

Can you answer janehart21’s question about Luggage?:

I’m flying into La Guardia tomorrow on American and then I have to transfer to Delta. I’m planning on carrying on my luggage, but since I’m group 4 to board I’m afraid there won’t be room in the overhead compartment. Is there anything specific I need to do to make sure my luggage makes it on the Delta flight if they force me to check it?

Best Carry On Luggage