The first time Anakin appeared to her, Leia was furious. After everything he had done ... after the torture and Alderaan how dare he think that she would even want to talk to him? Yes, he has saved the life of Luke, her brother, but that one action didn't make up for the years of atrocities that had been committed by him and in his name. It didn't make up for everything and everyone that she had lost because of him and his allegiance to the Dark Side. Luke may have seen redemption in his final actions in life, but Leia still couldn't let go of everything that had led up to that final battle. So many things wouldn’t have happened if it hadn’t been for him and she made her opinion of that known.
The second time Anakin appeared to her, Leia was more tired than anything. They had destroyed the second Death Star and had achieved freedom for most of the Galaxy, but that didn't mean the fight was over. There were still damages to repair and bands of fighters that were still loyal to the old Empire and were trying to do their own damage or trying to fill the vacuum of power that they believed the death of Emperor Palpatine had left behind. The Rebellion were now the New Republic, but that didn't mean that things were automatically perfect for everyone. There was still clean up to do and the task of convincing the multitude of star systems that made up their Galaxy that they didn't want to be in control of everything but wanted everyone to have their own voice.
The third time Anakin appeared to her, after she thought she had lost everything, Leia was finally ready to listen to what he had to say.