I think using max heaps is more confusing rather than using min heap, and also, min heaps don't require pushing again any of the intervals

from heapq import heappop, heappush


#class Interval:
#  def __init__(self, start, end):
#    self.start = start
#    self.end = end


class Solution:
  def findNextInterval(self, intervals):
    n = len(intervals)
    result = [-1] * n
    end_heap = []
    begin_heap = []

    for i in range(n):
      b, e = intervals[i].start, intervals[i].end

      heappush(end_heap, (e, i))
      heappush(begin_heap, (b, i))

    while end_heap:
      e, i = heappop(end_heap)

      while begin_heap and begin_heap[0][0] < e:
          heappop(begin_heap)

      if begin_heap and begin_heap[0][0] >= e:
          result[i] = begin_heap[0][1]
    
    return result