In the EPL there has been a history of unfairness that tarnished the name of game and sportsmanship. In the recent years though, there has been an equal oppurtunity for both players and fans in clubs to be equal with one another, without having to worry about prejudice towards each other.
It is important not to get carried away when thinking about parity in the EPL. There will never be the sort of parity that exists in the American NFL, where there is 50% or higher turnover in the playoffs every year. However, there is beginning to be a greater sense of parity in the middle ranks of the EPL. This is mostly due to the fact that the bar was set so low. Manchester United has dominated the league for more than two decades, and their challengers have been few and far between. The fact that Manchester City was able to win the EPL in 2012 (the first time in more than 40 years) shows that the ManU deathgrip on the EPL is beginning to ease.
Yes, there is parity in the EPL, because the matches are always close. Even the matches in Week 27, the most that anyone won by was 4 goals, which isn't much for an entire game of football. Hull City gave the best showing. Between all the teams, there is up and down, but it is not a great difference.
With the proven ability for poor teams to beat rich teams, this would prove that there is parity if concern is of money versus squad strength. The teams with lower paid players are still a real threat to those with the higher paid players. This ensures that every game is exciting without a significant difference in the ability to win based on budget.
There is definitely no parity in the EPL. Some clubs and teams in the European Premiere League have an unfair advantage over others due to the fact that they can afford better talented players than some of the smaller clubs. I think that is the reason why most of the time, there are really only 4 teams who are contenders.