The same letters, in the same order, can follow the initial letter in each set to complete the words. The added letters are different for each set.

1)
A _ _ _ _ _
C _ _ _ _ _
 I _ _ _ _ _

2)
D _ _ _
F _ _ _
H _ _ _
S _ _ _
T _ _ _
Y _ _ _

3)
B _ _ _ _
C _ _ _ _
M _ _ _ _
P _ _ _ _
R _ _ _ _
S _ _ _ _
T _ _ _ _

Answers:

1)
ARISES
CRISES
 IRISES

2)
DOUR
FOUR
HOUR
SOUR
TOUR
YOUR

3)
BOWER
COWER
MOWER
POWER
ROWER
SOWER
TOWER