Anaiya isn't the type to demand obedience when she can be polite. I'm also theorizing that 4 levels is the point at which most AS are willing to defer beyond politeness to a stronger sister, but still won't take outright commands. We've seen women 1-2 levels lower be quite forceful with stronger women. Sheriam never deferred to Elaida, Lelaine and Romanda, Verin never really deferred to Bera/Kiruna despite 3 levels gap, neither did Seonid. The Salidar 6 didn't defer to Romanda or Lelaine either and Beonin was a level 16 making her 3 levels below them.

I also suspect that deference between the strongest levels is different than with the weaker women. Most level 16/17/18/19 women encounter few significantly stronger sisters and thus are unaccustomed to deferring on a regular basis, let's face it there are only about 50 Aes Sedai level 15+ so the vast majority of the time any woman in the 19+ range isn't going to face situations where she is forced to defer. However, the weaker women like Cabriana at level 36 is almost habitually deferring and may defer to women only 2 levels stronger simply because she's used to deferring in general. We see this a little bit when Siuan is depowered and the Aes Sedai note that she has not adjusted well to her new situation. Basically Siuan doesn't really know how to defer anymore because she's been at the top of the social ladder since she became strong enough to ignore Citalia. But even she struggled with a woman 8 levels higher, Aeldine at level 27. Yet we see no deference between Leane and Siuan with only 1 level difference and Leane is noted as having adjusted remarkably well, but Leane's act of obviously open dislike for Siuan is accepted as OK despite her being weaker, this probably wouldn't be as accepted if the strength margin between them was wider.

Another example we have is Delana at level 18. She implied that she should have been forced to defer to Siuan because of the margin between them (5) levels. Yet we see that Felaana at level 17 is willing to stand up to level 14 Merean and level 15 Katerine with little difficultly. This implies 2-3 levels difference is not enough to command deference beyond simple social nicety. Whereas at 4 levels women begin to accept polite instructions and at 5 levels take direct orders and beyond that it seems weaker women are expected to do as they are told without comment. Kumira at level 24 is essentially silent with everyone except Daigian and she is 10 levels below Merise, 9 below Nesune, 6 levels below Corele and Saren and 4 below Samitsu. In turn Samistu is 5 levels below Sashalle and struggles despite being placed in command. Cadsuane commands deference from everyone and is 5 levels higher than Merise, but Moiraine thinks to herself that when she is at full strength she won't be as disadvantaged (i.e. only 4 levels allows for Moiraine's level to at least have the expectation of politeness from a level 9 woman giving orders). This is further backed up by Meilyn and Kerene being only 1 and 2 levels below Cadsuane and showing no deference to her.

Thus, I suspect Siuan and Moiraine needed to be a minimum of 5 levels below Citalia to accept her clear orders, yet they couldn't have been much weaker than this for Moiraine to think Duhara on level 23 would still need to show her deference ... Thus 4 levels higher than Duhara