This is the 9842nd most frequent Russian word.
авиакомпаниями
"Airlines" (instrumental plural form).
Here, 'авиакомпаниями' (airlines) is used in the instrumental plural form to indicate the means through which the action of flying is performed (flying through airlines).
Я часто летаю авиакомпаниями, которые предлагают низкие цены.
I often fly with airlines that offer low prices.
The word 'авиакомпаниями' (airlines) is used in the instrumental plural form to express the actors involved in the context of competition.
Между этими двумя авиакомпаниями существует жесткая конкуренция.
There is stiff competition between these two airlines.
In this sentence, 'авиакомпаниями' (airlines) is instrumental, used to indicate the entity with whom the negotiation or discussion is happening.