Who is greater than whom?

Question

From the fact that Levi was in Bavel, Rav derived that R' Efes passed away.

He derived it like this:

After Rebbi passed away, R' Efes took over Rebbi's position. Rav Chanina was equal (or greater) than R' Efes in Torah learning (but not age, which is why Rav Chanina had R' Efes take over), so he learned outside. He needed someone to learn with, so he learned with Levi. When R' Efes passed away, R' Chanina took over his original position, so Levi (who was equal or greater than R' Chanina) had to go somewhere else to learn.

So we see from hear that Levi ≥ R' Chanina ≥ R' Efes.

However, the Gemara asks how did Rav know that R' Efes passed away? Maybe R' Chanina passed away. The Gemara answers that Levi would go to R' Efes' shiur. In other words R' Efes > Levi.

How does this work out?

(Shabbas 59b)

Answer 1

Rashi mentions that besides the question of who was greater in Torah, age was also a factor.

Thus, the gemara says that Rav deduced that since Levi had come to Bavel it must be because R. Efes had died, and his old chavrusa R. Chaninah had taken over from R. Efes. And since R. Chaninah was not greater than Levi neither in Torah nor in years there was no reason to attend his shiur, and so he came to Bavel.

But it was not possible that R. Chaninah had died and because he had no chavrusa Levi came to Bavel. Because if that was the case then Levi would have attended the shiur of R. Efes since he was older than Levi even though he was not greater than Levi in Torah.

However, R. Chaninah himself did not attend the shiur of R. Efes even though R. Efes was older than him because, as Rashi explains, he was "chashuv" - more important. I think what Rashi means is that since Rebbi before he passed away had instructed R. Chaninah to take over and thereby had assigned great importance to R. Chaninah's Torah learning, (but R. Chaninah had instead allowed R. Efes to take over because he was older), it would have been a slight to the honor of the Torah for R. Chaninah to attend his shiur.