Alif Baa- pronouncing Alif

I have the book Alif-Baa and it goes through pronunciation for long
vowel Alif. It says the range of the sound is 'a' bat or 'a' as in
father. That is consistent with other books. But then in the examples
it pronounces most of the Alif as 'e' in bed.

In the next paragraph after the first drill it shows difference
between alif (long a) and fatha (short a) and states: alif range, 'a'
in bad to 'a' in father, fatha range- 'e' in bet to 'u' in but.

I thought fatha sounds like 'a' in cat or 'o' in top. And I thought
Alif was just a longer version like 'a' in cab (but a little longer)
and or 'a' in calm. (According to other books).

Will someone please clarify this sound. Thank you.

-Homer