Hybrid glasses connect the emerging field of metal-organic frameworks (MOFs) with the glass formation, amorphization and melting processes of these chemically versatile systems. Though inorganic zeolites collapse around the glass transition and melt at higher temperatures, the relationship between amorphization and melting has so far not been investigated. Here we show how heating MOFs of zeolitic topology first results in a low density 'perfect' glass, similar to those formed in ice, silicon and disaccharides. This order-order transition leads to a super-strong liquid of low fragility that dynamically controls collapse, before a subsequent order-disorder transition, which creates a more fragile high-density liquid. After crystallization to a dense phase, which can be remelted, subsequent quenching results in a bulk glass, virtually identical to the high-density phase. We provide evidence that the wide-ranging melting temperatures of zeolitic MOFs are related to their network topologies and opens up the possibility of 'melt-casting' MOF glasses.