I just did a quick search and some airlines use the 20# limit (it actually varied from 16# to 25# to no limit in some cases) in addition to a dimensional limit of the carrier. Regardless, the carrier must be of specific dimensions and it varies by airline and whether the carrier is rigid or soft.
There are also breed restrictions that come into play too.
Always best to check with the specific carrier for the most up to date information.
Here is a
link but I would still check with the individual carrier as this information may not be accurate. The carrier will have the final say.
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