'Debió haber', 'debe haber', or 'debería haber'?
What is the difference between the following?

Debe haber - this means 'it must have'
Debería haber - the means 'it should have'
Debió haber - ?

I am confused as to how to past tense use of 'deber' here differs to the present tense usage.

Somebody on another forum wrote that 'debió haber' means 'should have'. But if this is true, how is this any different to 'deberia haber'?

Question

'Debió haber', 'debe haber', or 'debería haber'?
What is the difference between the following?

Debe haber - this means 'it must have'
Debería haber - the means 'it should have'
Debió haber - ?

I am confused as to how to past tense use of 'deber' here differs to the present tense usage.

Somebody on another forum wrote that 'debió haber' means 'should have'. But if this is true, how is this any different to 'deberia haber'?

Answer

Aquí debe haber mucha agua: There must be a lot of water here. (present)
Aquí debería haber mucha agua: There should be a lot of water here. (conditional)
Aquí debió haber mucha agua: There must have been a lot of water here. (past)

Answer

Creo que más o menos podría ser así:

Debería haber = Would have
Debe haber o Debió haber = Should have / Must have (dependiendo del contexto y resto de la frase)

Answer

I'm not sure if there is a proper translation to it but "deberia haber" is a conditional phrase so i think that it is right to say that the translation is "it should have" but at the same time it means "debio haber" because in english you don't have that many conjugation as in spanish.

I hope I could help you, Happy New year! 
Saludos!