How do each of the section headings relate to the corresponding part of the story?

In Fahrenheit 451, each of the three section headings acts as an allusion to the events that it covers. Part one, for example, is called "The Hearth and the Salamander." The hearth is symbolic of Montag's home life, and in this chapter, the reader learns that Montag is becoming increasingly frustrated with this part of his life, as we see through the strained relationship with his wife, Mildred. Similarly, the salamander is symbolic of Montag's occupation as a fireman, because this is the name they give to their fire trucks.
Part two is called "The Sieve and the Sand," and this is an allusion to an incident that happened in Montag's childhood. Montag's cousin promised him a dime if he could fill a sieve with sand. Obviously, Montag failed in this task because it is impossible to stop the sand from falling through the sieve. Montag is reminded of this incident on his way to Faber's apartment. When he realizes that the messages contained in books are important, he wonders if you can retain the words in the books if you read them quickly enough.
Finally, the third section of the novel is called "Burning Bright," and this relates to the destruction of the city at the end of the story. The use of the word "bright" not only provides a visual image of the destruction, it also has positive connotations, suggesting that there is some hope for creating a new society that values books and education.