oomis: I’m living in EY nearly 29 years and my Ivrit/Lashon HaKodesh is much better than yours. ?????? m’avreir is a noun in modern Hebrew meaning a fan from the word ???? air. This word is not relevant to our discussion on Hilchos Yom Tov. ????? ma’avir means to transfer, as you correctly pointed out, and since it is permitted on Yom Tov you may turn ON your gas oven with a pilot light. ????? mavir is the verb you are looking for than means to ignite a fire and is forbidden on Yom Tov. It is used numerous times in Chumash, for example in Pashas Mishpatim ??? ???? ?????? ?? ????? However none of this is relevant the issue at hand of turning off the fire.
You didn’t read what I wrote. The problem is not that you are extinguishing the pilot flame, you are NOT, as you pointed out. The problem is that when you light the fire on the stove you have created a second larger flame on the burner and it is this flame that you are extinguishing, which is absolutely forbidden. If you would have looked at the sources I provided you would have seen that even making an existing flame smaller is forbidden on Yom Tov, except under specific circumstances.