For the most part, I have flown without a problem across the USA and to various countries in Europe with my folding bike packed within a soft sided, rolling 29" suitcase (only when traveling on low cost airlines such as Go! Easy Jet was I surcharged due to weight requirements). Regardless, if you are concerned about being surcharged for traveling with your Giatex, here are a few tips.

1. Check the airlines' size & weight restrictions in advance.
According to various airline officials, expect to pay extra when your bike exceeds predetermined weight or size restrictions. These restrictions vary by airline but are typically based upon the storage and weight limits of the planes flown by that airline. To avoid a nasty surprise, check the website of the airline you are traveling to discover their restrictions. Measure the total dimensions (length + width + height) of your bag/suitcase to confirm that it meets the requirements of the airline(s) you intend to fly. If the bag meets the size restrictions, weigh the bag with the bike inside to confirm that you also meet the airlines' weight restrictions (especially important when flying the low cost airlines of Europe and Asia). See baggage restrictions for domestic USA carriers.

2. Use curbside check-in.
Baggage porters earn a living from their tips & are less likely to assess baggage fees then check-in agents, particularly when there's the prospect of a tip.

3. Join a major bike club.
As a member of various bicycle clubs/advocacy groups, some airlines offer free or discounted carriage of your bike. Look at the benefits of some of the national/international bike clubs. If you like what you see, join up.

4. Don't volunteer that you are traveling with a bike.
Most airline agents realize that bike carrying surcharges were meant to apply to standard 26" bicycles; however, due to vague and open-ended airline baggage policies, some agents will try to charge you even if your bike meets the size and weight restrictions (while other agents will not). Therefore, the best advice is to be inconspicuous. Don't leave your bike helmet or other cycling related items in plain view at the check-in counter. Don't voluntarily tell the agent about the fabulous bike trip you are taking or that you just finished.

5. Be nice.
Check-in agents deal all day with frustrated/angry/agitated customers. If you are cheerful and mind your manners at check-in, you are far less likely to experience problems.

6. Ask for a manager.
If, despite your pleasant attitude, the agent attempts to assess a surcharge regardless that your bike bag meets the size & weight restrictions, ask for a manager. If you politely explain to management that you specifically purchased a bike and luggage that meets their baggage requirements, they should see reason and carry your bike free of charge.

7. Ask Customer Service for a refund.
If the check-in personnel demand a surcharge, maintain a record of the experience. Save your receipts and take down the names of agent(s) involved. After your trip, write a complaint to the customer service department for that airline. Even if you don't get your money back, you may get a discount on future travel.