In this example, all three words are used in pretty much the same way and are interchangeable.
But it doesn't always work that way. For instance, I might go and 'see' or 'view' a film, but I wouldn't go and 'look at' a film. Also, I might 'look at' a magazine - which means that I turn the pages and read or see what is inside; however, I wouldn't 'view' a magazine. I might 'see' a magazine, but that would mean that you noticed with your eyes that there was a magazine nearby, similar to 'I saw a monkey in the tree'.
Does that make sense? Hope it helps.