In The Pilgrim's Progress, how is Vanity Fair an allegory?
I think you meant "allegory" instead of "analogy," so I have corrected your question accordingly. Of course, it is important to realise how all of this exciting novel in some ways is an allegory about the Christian life and journey as Christians view the world. Let us consider how Bunyan himself describes Vanity Fair:
...they contrived to set up a fair; a fair wherein should be sold of all sorts of vanity, and that it should last all the year long. Therefore at this fair are all such merchandise sold: as houses, lands, trades, places, honours, preferments, titles, countries, kingdoms; lusts, pleasures, and delights of all sorts--as whores, bawds, wives, husbands, children, masters, servants, lives, blood, bodies, souls, silver, gold, pearls, precious stones, and what not.
We can therefore infer that Vanity Fair is meant to stand for the spirit of materialism and possessions in this age and how strongly they force us to focus on what is earthly as opposed to heavenly. The fact that it is open all year round and that everything is sold shows how strong commercialism is as a spirit in our age and what a temptation it us for us to focus on what is temporary rather than what is eternal.