This mirror comes down to who assembles their Eldrazi engine faster and who can disrupt the other's key artifacts and Urza's Saga. Nature's Claim answers their Vexing Bauble, Trinisphere, or a Saga-made Construct token cheaply. Grafdigger's Cage doesn't stop their Devourer of Destiny's cast-trigger exile but shuts off any reanimation shenanigans and blocks Emrakul from returning via graveyard effects. We already have Boseiju as a land, but the two copies of Boseiju in the mainboard are undercut in a mirror where both players want to keep their own lands; trim to make room since our own Cage/Pithing Needle plan is more proactive. Keep Kozilek's Command and Emrakul in since they are our own win conditions and removal against their identical threats.

Izzet Prowess wants to curve out cheap spells (Lava Dart, Lightning Bolt, Mutagenic Growth, Preordain) and go wide with prowess triggers; Trinisphere taxes all of these up to 3 mana, badly disrupting their tempo plan. Damping Sphere further punishes them for casting multiple cheap spells per turn by taxing each subsequent spell. Soulless Jailer is mostly a body to block Monastery Swiftspear and Dragon's Rage Channeler while incidentally shutting off Lava Dart's flashback, though its real value here is as a blocker. Boseiju is less impactful since they run few nonbasic lands or artifacts/enchantments worth blowing up, and Vexing Bauble is weak since most of their key spells (Bolt, Preordain, Iteration) are paid for with mana.

Esper Blink leans on Solitude and Orcish Bowmasters as efficient interaction plus Overlord of the Balemurk and Witch Enchanter/Flickerwisp value; Thief of Existence exiles a noncreature permanent like Teferi, Time Raveler or Kaito, Bane of Nightmares when it's cast, denying their blink/value engine a target and leaving them a draw-a-card downside when it leaves the battlefield. Soul-Guide Lantern proactively exiles a graveyard card before Emperor of Bones or Overlord of the Balemurk can use it, and can cycle away late. We cut the extra Vexing Baubles since this opponent pays mana for nearly everything.