I travel with my tackle frequently.
The regulations can vary with each airline. Delta is the worst. Their fees are the highest for oversized/overweight luggage.
Alaska Airlines is the best. They allow a rod tube of 84" to go through your check in luggage without a fee, and they only charge $50 for a piece of luggage that is over 50 pounds.
Delta charges $100 for the rod tube and $100 for the overweight bag.
If you decide to carry on some reels with line on them, or terminal tackle/lures, you may be in for a delay. Most airlines won't let you carry them on board. Put it in your check in luggage.
Some of the airlines will let you carry a reel on board with mono on it. Some don't allow "spectra" type lines.
The mono/spectra controversy continues even with the airlines!
Three piece rods in a tube can be carried on board. Check the individual airline regulations.
I've always found traveling with my tackle to be a breeze. Just do it right.
Moogie
I routinely ship 2 rods (each one piece, seven footers) in a tube, from NY to FLA, costs about $25 each way via UPS. If shipped at least 1 week in advance of your arrival, they can be shipped by land, which is safer than by air.