How does tom sawyer increase maturity? ?

To say that Tom matures is not to say that he becomes mature in The Adventures of Tom Sawyer (or afterwards).

The first example of Tom’s maturity is when he visits her aunt during his funeral.  He realizes that he has hurt her, and he feels bad.  For once Tom actually feels empathy for others.  He also feels sorry for Huck when he does not seem to have someone to miss him.

This was a new aspect of the thing. His smartness of the morning had seemed to Tom a good joke before, and very ingenious. It merely looked mean and shabby now. He hung his head and could not think of anything to say for a moment. Then he said: “Auntie, I wish I hadn't done it—but I didn't think.” (ch 19, p. 88)

The second example of Tom’s maturity is when he lies to the schoolmaster for Becky Thatcher.  When Tom jumps up to claim he was the one who ripped the schoolbook, taking Becky’s punishment, he surprises everyone- even himself!

The school stared in perplexity at this incredible folly. Tom stood a moment, to gather his dismembered faculties; and when he stepped forward to go to his punishment the surprise, the gratitude, the adoration that shone upon him out of poor Becky's eyes seemed pay enough for a hundred floggings. (ch 20, p. 92)

The final example of Tom’s maturity is when he tells the prosecutor about what really happened in the cemetery, despite his fear of Injun Joe.  Tom does the right thing, and tells the truth, because his conscience tells him to.

Since Tom's harassed conscience had managed to drive him to the lawyer's house by night and wring a dread tale from lips that had been sealed with the dismalest and most formidable of oaths, Huck's confidence in the human race was well-nigh obliterated. 

each poet admires poetry

they each admire poetry because they could just use an expression or verbally just say you but they both write in in poetry which shows they know how to write in poetry.

are you asking for an essay and whats the story?