
Patch 7.3a

Favorable matchup
Sivir answers Caitlyn's plan with wave clear and a Spell Shield that stops one important ability. She doesn't outrange Caitlyn's basic attacks: she gains value by preventing the siege and saving resources for a prepared trade.
Your first ability and the ricochets help you handle minions without stepping up for every basic attack. If you match the push, Caitlyn has less time to set traps under your tower. You need mana: spending your whole pool on poke leaves you with no answer to the next wave.
Spell Shield can answer an ability such as Caitlyn's first or a trap with the right timing. It doesn't block her basic attacks or automatically remove Headshot. The enemy support can also pop it before the main threat arrives.
Look for the trade when the wave is under control and Caitlyn has used her net, with your shield still available. If the enemy support still has their crowd control, don't walk up just to contest basic attacks.
As Caitlyn, pressure Sivir with basic attacks when she uses abilities on the wave, and don't give her a shield on an isolated ability. Coordinate crowd control with your support to pop her defense before the important threat. Keep your net if Sivir and her team can speed up and close the gap.

Execution matters
Ezreal can ease Caitlyn's pressure by farming from range and holding a defensive dash. It's an answer for surviving and contesting windows, not a promise to dominate the lane: minions and the wave push limit his first ability.
Your first ability lets you last-hit or poke from afar, but it hits the first target. If Caitlyn hides behind the wave, find another firing line or use the ability to farm; it doesn't pass through every minion to hit her.
Your third ability helps you reposition against an engage or a trap in your path. Use it before you're immobilized: it doesn't remove the immobilization of a trap you've already stepped on. Anticipating the catch lets you preserve health and go back to poking from a safe angle.
Poke from a clear line when Caitlyn commits to a last hit, and keep your third ability. You can be more aggressive if she spends her net and your support opens an engage, without dashing through a trap zone.
As Caitlyn, protect your last hits behind your minions and use wave pressure so Ezreal has to spend his shots on farming. Watch when he uses his third ability; that's your window to catch him with your support. If he stays safe, turn the push into tower damage and vision instead of forcing a chase.

Execution matters
Varus can contest Caitlyn outside her comfortable basic-attack trade with charged arrows and threaten an engage with his ultimate. He depends on landing shots and on the support matchup: Varus has no dash to fix bad positioning.
His charged first ability lets you poke from afar without contesting every basic attack with Caitlyn. The arrow passes through units, though its damage drops as it goes through them; it isn't blocked just by standing behind a minion. Look for a clean angle without leaving a protected position.
His ultimate can immobilize and makes your support's crowd control easier to land. The best window comes when Caitlyn has already used her net or has a limited escape. It doesn't instantly chain her whole team, and if it misses, Varus is still a marksman with no dash, exposed to the siege.
Charge an arrow when Caitlyn commits to a last hit or an ability. To go for the kill, wait until her net is down and your support can follow up the crowd control from your ultimate.
As Caitlyn, move sideways when you see Varus charging: minions can reduce the damage, but they don't stop the arrow completely. Save your net for a predictable threat and avoid sharing a narrow passage with allies when his ultimate is up. Pressure him with your support when he misses an arrow or his crowd control.