This mirror comes down to card quality and disruption; Duress strips their Thoughtseize, removal, or Culling Ritual before they can use it proactively, while the extra Culling Ritual and Withering Curse punish their low-curve creatures like Badgermole Cub, though neither one touches Professor Dellian Fel, so keep removal like Abrupt Decay and Go for the Throat in mind for the planeswalker's -3 and other threats. Trim the weakest small bodies (some Badgermole Cubs, a Sentinel, a Graveyard Trespasser) since both decks are grindy and card advantage/disruption outvalue marginal 2/2s, 3/3s and 3/4s. Keep Sheoldred, the Apocalypse and Unholy Annex in since they are premium mirror-breakers against an opponent with the same cards. Be mindful that the opponent also has Go Blank and Necromentia to attack your graveyard and hand, so sequence Thoughtseize and disruption early.

Izzet Cauldron relies on Hearth Elemental and Eddymurk Crab's graveyard-cost-reduction and delve-adjacent synergies, so Unlicensed Hearse exiles their graveyard to blunt those discounts while also growing into a real threat. Invoke Despair is excellent since it forces a creature sacrifice (hitting Hearth Elemental or Sunderflock) and can also strip an enchantment or planeswalker with no good answer from them. Trim the smaller, less impactful creatures that don't pressure their counterspell-heavy, grindy plan. Keep Thoughtseize and Abrupt Decay in to proactively strip their cheap interaction like Stubborn Denial before deploying bigger threats.

UBR is a value/control deck full of card advantage engines (Fable of the Mirror-Breaker, The Theorist, Jace Beleren) and reanimation targets (Atraxa, Valgavoth) that Go Blank punishes hard by stripping two cards and exiling their graveyard, cutting off Flashback and delve-fueled plays. Duress proactively strips removal or countermagic like Make Disappear before you commit threats. Trim some smaller creatures and the maindeck Culling Ritual, which is weak against a deck without many cheap permanents to blow up. Keep Thoughtseize and Sheoldred, the Apocalypse as your best disruption and clock against their grindy gameplan.