It's really up to you! I typically leave my turkey stock partially covered (with the lid kind of perched on top of the pot, leaving about 1/3 of the pot uncovered) while it cooks because I love the way it fills the house with its aroma. Because this stock cooks in just a few hours, you won't lose too much liquid to evaporation - plus, letting that little bit of the liquid evaporate as the broth cooks helps to concentrate the flavor for a richer final product! If you have kids running around, or if you're planning to let the broth simmer for a longer period of time, you can pop the lid on while it cooks.