Please note that if you are using the results of the blitz to pair only the first round of the rapid and then the results of the rapid to pair only the first round of the dual, then you have three different, albeit loosely linked, events of 8, 4 and 2 rounds rather than one event of 14 rounds. One way of doing that is to pair a 9th round of the blitz (never played) to get your round one rapid pairings and to pair a 5th round of the rapid (never played) to get your round one dual pairings.
Since you need to rate them separately anyway that tracks. If the blitz is actually four double-rounds (play each opponent once with White and once with Black) then it goes quicker and would essentially be only a four round Swiss.
If you want to keep all of the results from the prior time controls when making the new pairings then you will need to later split them up for rating purposes. Pair all 14 rounds and then make three copies. In one you delete rounds 9-14 and submit it for blitz rating. In another you convert the rounds 1-8 results to forfeit wins/losses and unplayed draws and then. after making a copy for the final step, you delete rounds 13-14 and submit it for rapid (quick-only) rating. In that copy with the converted rounds 1-8 results you also convert rounds 9-12 to forfeit wind/losses and unplated draws and submit it for dual rating (or regular only if you have something like a G/60;d10 time control). Pairing programs might not allow double rounds for only some of the rounds, so if the blitz are double-rounds while the others are not you would have to manually pair the second half of each double-round.
The k-factor of each section would be less than the k-factor for a 14-round Swiss but that is appropriate since each section would be in a different rating class.
For TD certification purposes the blitz would be a 4-(double) round or 8-round Swiss for a Category D blitz event (or higher category if there are 50+ actual players after ignoring any players who never played). The rapid would be a 2-(double) round or 4-round Swiss with the 2-double round not counting as any category or the 4-round counting as a category D quick event (or higher under the same conditions mentioned for blitz). The dual (or regular if the time control is long enough) would be a 2-round event that does not fall into any category.