People are acting as if Nagato has no knowledge what so ever of Itachi's abilities. As an acting leader of Akatsuki it is not illogical to say that he would have certain amount of knowledge about each member and this includes Itachi.
The fact that Nagato deduced Itachi's possession of Amaterasu from the air pressure just goes to show
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Nagato had prior knowledge about it. Therefore it would also be rather obvious about Itachi prowes in Genjutsu. Itachi using Amaterasu would be useless anyway since Nagato would be priory aware of its use.
Any possible damage done to Nagato's body is mechanically replaced by
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. Asura Path is not just there for attacks but it also provides a good solid defence as well as repairing abilities.
The use of Totsuka Sword and Yata Mirror requires Itachi to bring out Susano and Susano can be dealt with numerous ways.
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would be the ideal counter as you can't fully stop the dogs unless you stop the summoner, which is easier said then done against Nagato.
Does Itachi have good amount of knowledge about Nagato? Well from what we have seen in the manga the only time Itachi was present when an ability of Nagato was used when Deva Path used the body jutsu to hold off Team Guy. Other than that there has been no reference what so ever about Itachi's knowledge on it apart from that Nagato has Rinnegan and maybe myth stories about the Rinnegan.
There are numerous ways how Nagato can counter majority of Itachi's attacks but it can't be said for Itachi when its the other way round.