Pull the veins towards you so as to remove them without cutting them; you must "follow" them and accompany them, if necessary by passing your fingers through the flesh of the liver under the vein.
This is the first delicate moment of the recipe, and you must try not to forget any, or at least as little as possible. Your hands are very, very greasy, but you can use thin rubber gloves.
Note: We tend to say "nerve" and "denerver", but in fact there are no nerves in a liver, only veins.