Add canned tomatoes to a medium pot with water, dried chiles, garlic, and spices and bring to a simmer over low heat. Simmer, covered, for 15 minutes over very low heat.
Remove from heat and let the salsa steep, covered for 10 minutes.
Remove dried chiles and garlic from the mixture and transfer to a blender. Add fresh lime. I like to add one chile back to the mix (remove seeds first). It will add a very mild chile flavor to the salsa. You could add all three if you wanted or none.
Pulse mixture in a blender until it's a coarse consistency. I like it not too chunky.
Strain the salsa mixture through a metal sieve, separating the chunks from the water. Then add the liquid to the chunks until you reach the consistency you like. I like to add about 2/3s of the water back. That will leave you with a thin, but dippable, salsa.
If you want to eat the salsa immediately, chill it in a bowl with ice to cool it down fast. Otherwise store in the fridge for at least an hour to chill.
Once chilled, taste the salsa and adjust for salt to your liking. Serve with chips. Leftover salsa will keep fine in the fridge for a week or you can freeze it for longer storage.