Words are pronounced differently throughout the country - just about anything with an "a" in it, for example - but very few words are sometimes pronounced differently by the same person. Two of the most prominent, the two above, work from the same set of sounds. People generally say ant or aunt the same way in every context, but sometimes, and individual aunts will be referred to by the other pronunciation because well, that's their name. This happens more often when two sides of a family have a different preference. The children grow up with a preferred pronunciation for the generic, but some of both pronunciations for individuals. There is also the even more regional Aint or even Ayunt in the south, such as Andy of Mayberry's Aint Bee. Both sides of my family used the traditional Boston-area aunt-with-a-"u" version, but my mother's second husband came from North Haven and used Ant. I found it jarring when he would refer to my mother's aunt as Ant Sal, because...because that wasn't her name. Of course Aunt Sal wasn't her name either. Her name was Selma, and Aunt was a title. And yet, when you are an aunt or an uncle it is your name to some people, and that might even start extending to friends and neighbors as well.
Pecan is even more complicated, because not only the vowel sound can vary, but also which syllable is accented. Most people have a single pronunciation for every use of the word, puh-CAHN, or pee-CAHN, or PEE-can, or pee-CAN. Others vary it depending on whether they are talking about the pie, the tree, or the plural of them in the bag at the store. Even people who use one of the "can" variants in every other setting might shop for pecahns at the store, and so buy pecahns to make a pecan pie. The pie is particularly tricky, because for some it is one of those phrases in which none of the syllables is accented: Pee Can Pie or Pee Cahn Pie. Even those who accent one syllable or another in the phrase tend to do so in an underplayed manner. Others will change their pronunciation if there is a modifier in the front, especially "Georgia." Because that's their name, don't you know, regardless of what the nut is called in general.
The other most common word with variable pronunciation in the same mouth is "route." One grows up with a preferred pronunciation, but might visit a place for vacation a few times as a child and adopt the other for a specific road. Rout 17 is the best root to go.