There is a good chance you might have to carry you luggage. Depends on how short is your connections and if the two airlines have an interline agreement.(Example: If your travelleing Lufthansa and connecting with Jet Blue then you dont have to worry about your bag)If your connection is around an hour pick your bag up and recheck with Delta because it might not make the flight (my experiance). The good news is that terminal 3 is 100ft walking distance from terminal 1 and yes you can bring the cart. If its snowing like today, there is an Air Train to Term. 3, it takes 1 min.
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There is a good chance you