What inspires Tom finally to apologise to Becky? How is Tom beginning to show a different side to his character?

After Aunt Polly kisses Tom good-bye, his moods are lifted. Seeing Becky Thatcher, he runs to her and apologizes for ignoring her and asks to "please make up." But Becky, still furious, simply tosses her head and passes on, sending Tom into a rage. Still, this shows Tom is maturing a little.