Igros Moshe (Y.D. 3:88): Is it permitted to argue with the words of our Sages in public – even in their communities? You are concerned about the permissibility of moving to Bnei Brak because there are times when you will be disagreeing with the Chazon Ish zt”l. I really don’t understand why you are concerned. In fact the opposite is true. It is in fact showing respect to the Chazon Ish zt”l by mentioning his Torah view and examining his words – even though you don’t end up agreeing with him. It would be inconceivable to the Chazon Ish zt”l that there shouldn’t be a talmid chachom who disagreed with him. It is simply not possible that he would be bothered by this. In fact the opposite is true. He loved truth and peace as it says in (Yevamos 14b) concerning the dispute between Beis Shammai and Beis Hillel. In fact the idea that the deceased talmid chachom gets pleasure from discussion of his Torah work – is even when it is disputed. However, obviously it has to be mentioned respectfully. This that Rabbi Yehoshua suffered (Chagiga 28b) was not because he questioned the words of Beis Shammai but because he spoke in an inappropriate manner against them. But when done respectfully there is absolutely no problem - either with questioning the words of a talmid chachom or disagreeing with them. In fact not only is it permitted but we see from Bava Basra (130) that Rava told his students that they were not allowed to rule according to a view of his that they disagreed with since a judge can only rule based on how he sees things. The same applies with issurim…. As long as a student could not find an explanation for difficulties he had with Rava’s understanding he is not allowed to make a ruling in accord with it - even though Rava was his teacher.. If that were true with Rava and his students than it is surely true that one should not be concerned about questioning and disagreeing with gedolim of our generation – even the highest level gadol – as long as it is done in a respectful manner. Therefore there is absolutely no basis for concern or to feel it is inappropriate to remain in Bnei Brak and to give lectures. Just the opposite is true, the Chazon Ish with be your advocate in Heaven because you study his Torah works in a serious manner.