Benetton Treviso, on the other hand, have found life tough and are still looking for a first win of the campaign.
But Anayi, who started his new role in October, is optimistic that a pair of competitive derbies can inspire Italian rugby and help the game grow in the country.
"PRO12 derbies must be the starting point to keep on developing PRO12 in Italy," said Anayi at a presentation of the two Italian derbies in Milan.
"A positive, passionate rivalry between Benetton and Zebre is crucial for that and it also represents a brilliant tool to engage the media and have them behind the championship.
"I'm confident that working alongside with FIR and Guinness we can give all together a boost to the PRO12 and Italian rugby in general. We hope today marks the start of a new era for PRO12.
"It's a real PRO12 today, not a Celtic League anymore and it's important that the two Italian teams are getting more and more competitive. Together with FIR, coaches and captains we want local derbies to be a milestone in the Italian rugby season."
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