NZ are now 'slight' favourites to win this test series, believe it or not, mainly because Indian spinners have been rendered ineffective against the likes of Conway & Ravindra who both had intense training sessions at CSK ahead of the series on both red soil and black soil pitches against off spinners, conventional left armers as well as left arm wrist spinners. They came as ready to take down the spinners as anyone could be.
From India's POV, the biggest worry from the 1st test is not the batting but the bowling, which looked toothless during Southee Ravindra partnership as well as against NZ's top order. Besides that, Pant will likely miss at least the next test if not the rest of the series, which is a huge blow because of his ability against spin and being a left hander in a lineup full of right handers.
India made a number of blunders in terms of selection and decisions. Siraj now must make way for Akash Deep, who is more accurate and probing and better bowler against left handers too. Also Washington Sundar has been added to India's squad, which suggests that they may be considering to play Axar or Sundar in the next match. Perhaps Ashwin is not 100% as he looked well below his best. I wouldn't be surprised to see a change in the spin attack, otherwise there's no reason to add Sundar to the squad.
Unless India produces proper spinning wickets with nothing much in it for seamers, NZ are slight favourites to win. Also considering that the last test happens to be in Mumbai which always has assistance for seamers. Plus there's been monsoon rain all around this Pune and Mumbai region recently (though it has just cleared now) so I doubt soil/pitches can be made dry enough to prepare proper turners.
So don't be surprised if India loses this series. The way the TM has been going on about playing aggressive cricket has already proved costly as a number of batsmen have thrown their wickets. No team can afford to do that in Test Cricket where a single wicket can trigger a fatal collapse as we have seen. So I don't see things going that well. If India do win the next two tests- these would be very hard fought difficult wins.