Nebulizers, CPAPs, BiPAPs and APAPs are allowed in carry-on bags but must be removed from the carrying case and undergo X-ray screening. Facemasks and tubing may remain in the case.
You may provide a clear plastic bag to place the device in for X-ray screening. A TSA officer may need to remove the device from the bag to test it for traces of explosives.
Liquids associated with nebulizers are exempt from the 3-1-1 liquids rule, in reasonable quantities. For more information, see TSA special procedures.
Devices containing lithium metal or lithium ion batteries should be carried in carry-on baggage. Most other consumer electronic devices containing batteries are allowed in carry-on and checked baggage.
For more information to portable electronic devices, see the FAA regulations.