You apply all of them
This is explained under Multiple Uses of Edge and Effort (Cypher System Rulebook, pg.17):
You can use Edge for a particular stat only once per action. For example, if you apply Effort to a Might attack roll and to your damage, you can use your Might Edge to reduce the cost of one of those uses of Effort, not both. If you spend 1 Intellect point to activate your mind blast and one level of Effort to decrease the difficulty of the attack roll, you can use your Intellect Edge to reduce the cost of one of those things, not both.
The use of the wording "particular stat" makes it seem like you could use different Edges (Might, Speed or Intellect) for different pools in a single action, for different stats. There are very few situations where you may apply two different Edges to the same action, this being one of those.
However, note that you play only apply Edge to Actions, not everything that costs you points from your ability pools. Successive Attack is not an action, it is an Enabler, which you cannot apply Edge to. They are always part of another action and should increase the total ability pool points used for that action. It will cost you 2 points of Speed to activate the second attack. So, if you already used your Speed edge to reduce another cost, you cannot apply it again to reduce the cost of Successive Attack, as you may only apply your Edge once per action.
Some special abilities allow you to perform a familiar action—one that you can already do—in a different way. For example, an ability might let you wear heavy armor, reduce the difficulty of Speed defense rolls, or add 2 points of fire damage to your weapon damage. These abilities are called enablers. Using one of these abilities is
not considered an action.
Basically, the way to look at how Edge works is to sum the total cost of everything you used for that action, such as Effort and ability costs, then apply your Edges to reduce them before actually making the necessary checks to see if you were successful or not.