This is another variation of the classic problem of changing one word into another. Instead of changing one word into another one letter at a time for each step, this variation alternates each step by anagramming one word into another.

For example: CAT to DOG can occur as such:
CAT
ACT (anagram)
ANT (letter change)
TAN (anagram)
TON (letter change)
NOT (anagram)
NOD (letter change)
DON (anagram)
DOG (letter change)

Either the letter change or the anagram may occur first, but must then alternate.

I offer four challenges. In the fewest steps,
1) transform EARTH to WATER,
2) convert WIND to FIRE,
3) cross from RIVER to SHORE, and
4) transmute LEAD to GOLD.

In each case, the beginning word shown only once:

earth ...

hater
cater
crate
orate
oater
water
------- 6
hater
cater
crate
prate
pater
water
------- 6
hater
cater
trace
trade
dater
water
------- 6
hater
dater
rated
ratel
later
water
------- 6
hater
dater
tared
wared
wader
water
------- 6
hater
dater
trade
trace
cater
water
------- 6
hater
dater
tread
treat
tater
water
------- 6
hater
later
alter
apter
pater
water
------- 6
hater
later
ratel
rated
dater
water
------- 6
hater
later
taler
tamer
mater
water
------- 6
hater
later
taler
taper
pater
water
------- 6
hater
later
taler
tawer
water
------- 5
hater
mater
tamer
taler
later
water
------- 6
hater
mater
tamer
taper
pater
water
------- 6
hater
mater
tamer
tawer
water
------- 5
hater
oater
orate
crate
cater
water
------- 6
hater
oater
orate
prate
pater
water
------- 6
hater
pater
apter
alter
later
water
------- 6
hater
pater
prate
crate
cater
water
------- 6
hater
pater
prate
orate
oater
water
------- 6
hater
pater
taper
taler
later
water
------- 6
hater
pater
taper
tamer
mater
water
------- 6
hater
pater
taper
tawer
water
------- 5
hater
rater
terra
tetra
tater
water
------- 6
hater
tater
tetra
terra
rater
water
------- 6
hater
tater
treat
tread
dater
water
------- 6
hater
water
------- 2
heart
heard
hared
tared
dater
water
------- 6
heart
heard
hared
wared
wader
water
------- 6
heart
peart
apter
alter
later
water
------- 6
heart
peart
pater
water
------- 4
heart
peart
prate
crate
cater
water
------- 6
heart
peart
prate
orate
oater
water
------- 6
heart
peart
taper
taler
later
water
------- 6
heart
peart
taper
tamer
mater
water
------- 6
heart
peart
taper
tawer
water
------- 5

wind ...

kind
dink
dine
nide
ride
dire
fire
------- 7

river ...

diver
rived
rives
vires
hires
shire
shore
------- 7
ricer
crier
cries
cires
cores
score
shore
------- 7
ricer
crier
cries
cires
hires
shire
shore
------- 7
rifer
frier
fries
fires
hires
shire
shore
------- 7
riper
prier
pries
prise
prose
spore
shore
------- 7
riper
prier
pries
ripes
ropes
spore
shore
------- 7
riper
prier
pries
spier
shier
shire
shore
------- 7
rived
diver
siver
vires
hires
shire
shore
------- 7
rives
siver
siker
keirs
heirs
shire
shore
------- 7
rives
siver
siker
skier
shier
shire
shore
------- 7
rives
viers
kiers
keirs
heirs
shire
shore
------- 7
rives
viers
kiers
skier
shier
shire
shore
------- 7
rives
viers
liers
slier
shier
shire
shore
------- 7
rives
viers
piers
prise
prose
spore
shore
------- 7
rives
viers
piers
ripes
ropes
spore
shore
------- 7
rives
viers
piers
spier
shier
shire
shore
------- 7
rives
viers
tiers
rites
rotes
store
shore
------- 7
rives
viers
tiers
tires
hires
shire
shore
------- 7
rives
viers
tiers
tires
tores
store
shore
------- 7
rives
vires
hires
heirs
hears
share
shore
------- 7
rives
vires
hires
shier
shoer
shore
------- 6
rives
vires
hires
shire
shore
------- 5
rives
vires
tires
rites
rotes
store
shore
------- 7
rives
vires
wires
weirs
heirs
shire
shore
------- 7
siver
rives
rices
cires
cores
score
shore
------- 7
siver
rives
rices
cires
hires
shire
shore
------- 7
siver
rives
riles
slier
shier
shire
shore
------- 7
siver
rives
rimes
mires
hires
shire
shore
------- 7
siver
rives
ripes
prise
prose
spore
shore
------- 7
siver
rives
ripes
spier
shier
shire
shore
------- 7
siver
rives
rises
sires
hires
shire
shore
------- 7
siver
rives
rites
tires
hires
shire
shore
------- 7
siver
rives
rites
tires
tores
store
shore
------- 7
siver
viers
kiers
keirs
heirs
shire
shore
------- 7
siver
viers
kiers
skier
shier
shire
shore
------- 7
siver
viers
liers
slier
shier
shire
shore
------- 7
siver
viers
piers
prise
prose
spore
shore
------- 7
siver
viers
piers
ripes
ropes
spore
shore
------- 7
siver
viers
piers
spier
shier
shire
shore
------- 7
siver
viers
tiers
rites
rotes
store
shore
------- 7
siver
viers
tiers
tires
hires
shire
shore
------- 7
siver
viers
tiers
tires
tores
store
shore
------- 7
siver
vires
hires
heirs
hears
share
shore
------- 7
siver
vires
hires
shier
shoer
shore
------- 6
siver
vires
hires
shire
shore
------- 5
siver
vires
tires
rites
rotes
store
shore
------- 7
siver
vires
wires
weirs
heirs
shire
shore
------- 7

lead ...

bead
abed
aged
gaed
gled
geld
gold
------- 7
lade
lads
dals
dols
sold
gold
------- 6
lade
lode
dole
dols
sold
gold
------- 6
lade
lode
dole
dolt
told
gold
------- 6
leas
lase
lose
oles
olds
sold
gold
------- 7
leas
sale
sole
oles
olds
sold
gold
------- 7
leud
lude
lode
dole
dols
sold
gold
------- 7
leud
lude
lode
dole
dolt
told
gold
------- 7