The best replacement for heavy period is early miscarriage.

The best alternatives to heavy period are rated as following:
★★★★★  early miscarriage
★★★★  miscarriage
★★★  hemorrhage
★★  hemorrhaging
★  chemical pregnancy
  light period

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Speaking about heavy period, one probably shouldn't forget about no cramps.

Other search terms related to heavy period and their ratings are:
★★★★★ no cramps
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heavy period
early miscarriage
miscarriage