The word desvelaba is the imperfect form of desvelar in the first person singular. There are other translations for this conjugation.
See the full desvelar conjugation

desvelar

Sí, habría odiado ver que la relación con Noelle se desvelaba.
Yeah, she would have hated seeing that relationship unfold with Noelle.
De las noches en que se desvelaba preocupada porque yo no volviera a casa.
All the nights she sat up worried I'd never make it home.
El mes pasado la Comisión desvelaba su nueva "Agenda para un turismo europeo sostenible y competitivo".
The Commission unveiled its new 'Agenda for a sustainable and competitive European tourism' last month.
El Padre Oscuro se enfureció al ver que se desvelaba tan fácilmente su verdadera naturaleza.
The Dark Father was enraged to see his nature revealed so easily.
Esta misma encuesta también desvelaba que el Parlamento inspiraba la mayor confianza de los encuestados.
The same poll also found that Parliament inspired the most confidence in the respondents.
En la pasada edición de la Feria de Verona ya se pudo ver un prototipo en pista pero hace unas horas Maurizio Ferrari desvelaba a través del portal autopiste.info las imágenes del despiece completo de este nuevo modelo.
In the last Verona Fair edition, a prototype could already be seen on the track, but a few hours ago Maurizio Ferrari unveiled the images of the complete exploded view of this new model through autopiste.info website.
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