What the effects react to
Acceleration
Acceleration entities trigger on Rush, the fast-attack state, and pay out in Attack Speed and Attack. 14 relics and items are built on it: 14 relics and 0 items.
Updated for patch 0.5.10
How long a Rush lasts
Rush abilities have a duration, and the relics that extend it form a quest ladder: Acceleration Accumulator adds 1 second after 2 Rush triggers, Acceleration Vessel 2 after 4, Acceleration Conduit 3 after 6 and Acceleration Ascendancy 4 after 15, ten seconds once all four are complete. On a single hero, Temporal Accelerator adds 5 seconds, Eye of Haste 3, and Hasty Ring 2 once Rush has triggered 3 times, while Ming under The Enlightened adds 2 per rank.
Two heroes reopen their windows instead of stretching them. Nyx refreshes all her Rush abilities every 12 auto attacks, and since 0.5.8 a refresh keeps the stacks she has already built. Rip refreshes his the first time he or an adjacent enemy drops below 50% Max HP.
Per-trigger payouts
The rest of the family pays per trigger or for a fixed window. Acceleration Fluctuator gives heroes 10 Attack Speed and 10 Attack on every Rush trigger and Acceleration Reactor 5 Crit and 10 Attack Speed; Acceleration Lattice regenerates 25 HP/S for Rush (10), and Acceleration Immunizer makes heroes immune to damage for Rush (2). Acceleration Legacy Crystal combines the two, adding 1% basic stats per two Rush triggers this game for Rush (8). The same count builds on Rip's The Glutton, 33 Max HP per trigger, on Crown of Haste, 1 Attack and 8 Max HP, and on the Duelist upgrade Rush Dynamo, 1 Attack Speed per Rush trigger this game.
Eight of eleven relic slots
Eight of the eleven relics in Rush Duelists come from this family, Accumulator, Vessel and Conduit among them, and Rush Shard Gen Duelists copies that list. The other three, Trigger Safeguard Activator, Alignment Ascendancy and Temporal Alignment Crystal, also respond to Stall triggers. Vessel and Legacy Crystal are the only Acceleration relics at A, each in three of the nine builds.
Accumulator has asked for 2 triggers instead of 3 since 0.5.5, the patch that cut Acceleration Resonator from 250 Shields per trigger to 200, and Legacy Crystal's window grew from Rush (6) to Rush (8) in 0.5.3. Acceleration Prism, 15 Crit per trigger, fired on Stall triggers until 0.5.8 and now answers Rush as its text says.
Relics and items that scale with Acceleration
Acceleration FluctuatorUniqueOn Rush trigger, give Heroes 10 Attack Speed and 10 Attack.
Acceleration ResonatorUniqueOn Rush trigger, Heroes gain 200 Shields.
Acceleration AccumulatorUniqueQuest: Trigger Rush 2 times. Rewards: Rush abilities last 1 second longer.
Acceleration LatticeCommonFor Rush (10), Heroes gain 25 HP/S.
Acceleration VesselCommonQuest: Trigger Rush 4 times. Rewards: Rush abilities last 2 seconds longer.
Acceleration NexusRareEvery 2 Rush triggers, gain 1 Shard.
Acceleration ReactorRareOn Rush trigger, give Heroes 5 Crit and 10 Attack Speed.
Acceleration ConduitRareQuest: Trigger Rush 6 times. Rewards: Rush abilities last 3 seconds longer.
Acceleration AscendancyEpicQuest: Trigger Rush 15 times. Rewards: Rush abilities last 4 seconds longer.
Acceleration ImmunizerEpicFor Rush (2), Heroes are immune to damage.
Acceleration PrismEpicOn Rush trigger, give Heroes 15 Crit.
Acceleration FiligreeEpicOn kill for Rush (20), gain 12 Shards.
Acceleration MandateLegendary QuestQuest: Trigger Rush 25 times. Rewards: Increase your team size by 1 (Max: 5).
Acceleration Legacy CrystalLegendaryFor Rush (8), Heroes gain +1% basic stats for every 2 times you've triggered Rush this game.