Just because words are in sequence does not necessarily require that they are unequal. Happiness can not be pursued without liberty and some believe that life is not valid without liberty ("Give me liberty or give me death"). Patrick Henry seemed to believe in the equality of at least life and liberty and we hold him to be an American hero.
If you think words don't mean anything, I pity you.
The founders of this great Republic gave us the phrase
"Life, liberty and the pursuit of happiness"
Let me put a finer point on this.
One can pursue happiness, if they do not possess liberty.
One can not have liberty, if some one takes their life.